1
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Li J, Ionides EL, King AA, Pascual M, Ning N. Inference on spatiotemporal dynamics for coupled biological populations. J R Soc Interface 2024; 21:20240217. [PMID: 38981516 DOI: 10.1098/rsif.2024.0217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2024] [Accepted: 06/07/2024] [Indexed: 07/11/2024] Open
Abstract
Mathematical models in ecology and epidemiology must be consistent with observed data in order to generate reliable knowledge and evidence-based policy. Metapopulation systems, which consist of a network of connected sub-populations, pose technical challenges in statistical inference owing to nonlinear, stochastic interactions. Numerical difficulties encountered in conducting inference can obstruct the core scientific questions concerning the link between the mathematical models and the data. Recently, an algorithm has been proposed that enables computationally tractable likelihood-based inference for high-dimensional partially observed stochastic dynamic models of metapopulation systems. We use this algorithm to build a statistically principled data analysis workflow for metapopulation systems. Via a case study of COVID-19, we show how this workflow addresses the limitations of previous approaches. The COVID-19 pandemic provides a situation where mathematical models and their policy implications are widely visible, and we revisit an influential metapopulation model used to inform basic epidemiological understanding early in the pandemic. Our methods support self-critical data analysis, enabling us to identify and address model weaknesses, leading to a new model with substantially improved statistical fit and parameter identifiability. Our results suggest that the lockdown initiated on 23 January 2020 in China was more effective than previously thought.
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Affiliation(s)
- Jifan Li
- Department of Statistics, Texas A&M University, College Station, TX 77843, USA
| | - Edward L Ionides
- Department of Statistics, University of Michigan, Ann Arbor, MI 48109, USA
| | - Aaron A King
- Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109, USA
- Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA
- Santa Fe Institute, Santa Fe, NM 87501, USA
| | - Mercedes Pascual
- Santa Fe Institute, Santa Fe, NM 87501, USA
- Departments of Biology and Environmental Studies, New York University, NY 10012, USA
| | - Ning Ning
- Department of Statistics, Texas A&M University, College Station, TX 77843, USA
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2
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Wheeler J, Rosengart A, Jiang Z, Tan K, Treutle N, Ionides EL. Informing policy via dynamic models: Cholera in Haiti. PLoS Comput Biol 2024; 20:e1012032. [PMID: 38683863 PMCID: PMC11081515 DOI: 10.1371/journal.pcbi.1012032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2023] [Revised: 05/09/2024] [Accepted: 03/29/2024] [Indexed: 05/02/2024] Open
Abstract
Public health decisions must be made about when and how to implement interventions to control an infectious disease epidemic. These decisions should be informed by data on the epidemic as well as current understanding about the transmission dynamics. Such decisions can be posed as statistical questions about scientifically motivated dynamic models. Thus, we encounter the methodological task of building credible, data-informed decisions based on stochastic, partially observed, nonlinear dynamic models. This necessitates addressing the tradeoff between biological fidelity and model simplicity, and the reality of misspecification for models at all levels of complexity. We assess current methodological approaches to these issues via a case study of the 2010-2019 cholera epidemic in Haiti. We consider three dynamic models developed by expert teams to advise on vaccination policies. We evaluate previous methods used for fitting these models, and we demonstrate modified data analysis strategies leading to improved statistical fit. Specifically, we present approaches for diagnosing model misspecification and the consequent development of improved models. Additionally, we demonstrate the utility of recent advances in likelihood maximization for high-dimensional nonlinear dynamic models, enabling likelihood-based inference for spatiotemporal incidence data using this class of models. Our workflow is reproducible and extendable, facilitating future investigations of this disease system.
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Affiliation(s)
- Jesse Wheeler
- Statistics Department, University of Michigan, Ann Arbor, Michigan, United States of America
| | - AnnaElaine Rosengart
- Statistics and Data Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States of America
| | - Zhuoxun Jiang
- Statistics Department, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Kevin Tan
- Wharton Statistics and Data Science, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
| | - Noah Treutle
- Statistics Department, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Edward L. Ionides
- Statistics Department, University of Michigan, Ann Arbor, Michigan, United States of America
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3
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Andrade J, Duggan J. Anchoring the mean generation time in the SEIR to mitigate biases in ℜ 0 estimates due to uncertainty in the distribution of the epidemiological delays. ROYAL SOCIETY OPEN SCIENCE 2023; 10:230515. [PMID: 37538746 PMCID: PMC10394422 DOI: 10.1098/rsos.230515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 07/13/2023] [Indexed: 08/05/2023]
Abstract
The basic reproduction number, ℜ 0 , is of paramount importance in the study of infectious disease dynamics. Primarily, ℜ 0 serves as an indicator of the transmission potential of an emerging infectious disease and the effort required to control the invading pathogen. However, its estimates from compartmental models are strongly conditioned by assumptions in the model structure, such as the distributions of the latent and infectious periods (epidemiological delays). To further complicate matters, models with dissimilar delay structures produce equivalent incidence dynamics. Following a simulation study, we reveal that the nature of such equivalency stems from a linear relationship between ℜ 0 and the mean generation time, along with adjustments to other parameters in the model. Leveraging this knowledge, we propose and successfully test an alternative parametrization of the SEIR model that produces accurate ℜ 0 estimates regardless of the distribution of the epidemiological delays, at the expense of biases in other quantities deemed of lesser importance. We further explore this approach's robustness by testing various transmissibility levels, generation times and data fidelity (overdispersion). Finally, we apply the proposed approach to data from the 1918 influenza pandemic. We anticipate that this work will mitigate biases in estimating ℜ 0 .
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Affiliation(s)
- Jair Andrade
- Data Science Institute and School of Computer Science, University of Galway, Galway, Republic of Ireland
| | - Jim Duggan
- Insight Centre for Data Analytics and School of Computer Science, University of Galway, Galway, Republic of Ireland
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4
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Gourieroux C, Jasiak J. Temporally Local Maximum Likelihood with Application to SIS Model. JOURNAL OF TIME SERIES ECONOMETRICS 2023; 15:151-198. [PMID: 38155754 PMCID: PMC10752238 DOI: 10.1515/jtse-2022-0016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2022] [Revised: 10/31/2022] [Accepted: 02/07/2023] [Indexed: 12/30/2023]
Abstract
The parametric estimators applied by rolling are commonly used for the analysis of time series with nonlinear patterns, including time varying parameters and local trends. This paper examines the properties of rolling estimators in the class of temporally local maximum likelihood (TLML) estimators. We consider the TLML estimators of (a) constant parameters, (b) stochastic, stationary parameters and (c) parameters with the ultra-long run (ULR) dynamics bridging the gap between the constant and stochastic parameters. We show that the weights used in the TLML estimators have a strong impact on the inference. For illustration, we provide a simulation study of the epidemiological susceptible-infected-susceptible (SIS) model, which explores the finite sample performance of TLML estimators of a time varying contagion parameter.
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Affiliation(s)
- Christian Gourieroux
- University of Toronto, Toronto, Canada
- Toulouse School of Economics (TSE), Toulouse, France
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5
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Wu D, Petousis-Harris H, Paynter J, Suresh V, Maclaren OJ. Likelihood-based estimation and prediction for a measles outbreak in Samoa. Infect Dis Model 2023; 8:212-227. [PMID: 36824221 PMCID: PMC9941367 DOI: 10.1016/j.idm.2023.01.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Revised: 01/19/2023] [Accepted: 01/29/2023] [Indexed: 02/05/2023] Open
Abstract
Prediction of the progression of an infectious disease outbreak is important for planning and coordinating a response. Differential equations are often used to model an epidemic outbreak's behaviour but are challenging to parameterise. Furthermore, these models can suffer from misspecification, which biases predictions and parameter estimates. Stochastic models can help with misspecification but are even more expensive to simulate and perform inference with. Here, we develop an explicitly likelihood-based variation of the generalised profiling method as a tool for prediction and inference under model misspecification. Our approach allows us to carry out identifiability analysis and uncertainty quantification using profile likelihood-based methods without the need for marginalisation. We provide justification for this approach by introducing a new interpretation of the model approximation component as a stochastic constraint. This preserves the rationale for using profiling rather than integration to remove nuisance parameters while also providing a link back to stochastic models. We applied an initial version of this method during an outbreak of measles in Samoa in 2019-2020 and found that it achieved relatively fast, accurate predictions. Here we present the most recent version of our method and its application to this measles outbreak, along with additional validation.
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Affiliation(s)
- David Wu
- Department of Engineering Science, University of Auckland, Grafton, Auckland, 1010, New Zealand
| | - Helen Petousis-Harris
- Department of General Practice and Primary Health Care, University of Auckland, Grafton, Auckland, 1023, New Zealand
| | - Janine Paynter
- Department of General Practice and Primary Health Care, University of Auckland, Grafton, Auckland, 1023, New Zealand
| | - Vinod Suresh
- Department of Engineering Science, University of Auckland, Grafton, Auckland, 1010, New Zealand
- Auckland Bioengineering Institute, University of Auckland, Grafton, Auckland, 1010, New Zealand
| | - Oliver J. Maclaren
- Department of Engineering Science, University of Auckland, Grafton, Auckland, 1010, New Zealand
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6
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Fisher A, Xu H, He D, Wang X. Effects of vaccination on mitigating COVID-19 outbreaks: a conceptual modeling approach. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:4816-4837. [PMID: 36896524 DOI: 10.3934/mbe.2023223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
This paper is devoted to investigating the impact of vaccination on mitigating COVID-19 outbreaks. In this work, we propose a compartmental epidemic ordinary differential equation model, which extends the previous so-called SEIRD model [1,2,3,4] by incorporating the birth and death of the population, disease-induced mortality and waning immunity, and adding a vaccinated compartment to account for vaccination. Firstly, we perform a mathematical analysis for this model in a special case where the disease transmission is homogeneous and vaccination program is periodic in time. In particular, we define the basic reproduction number $ \mathcal{R}_0 $ for this system and establish a threshold type of result on the global dynamics in terms of $ \mathcal{R}_0 $. Secondly, we fit our model into multiple COVID-19 waves in four locations including Hong Kong, Singapore, Japan, and South Korea and then forecast the trend of COVID-19 by the end of 2022. Finally, we study the effects of vaccination again the ongoing pandemic by numerically computing the basic reproduction number $ \mathcal{R}_0 $ under different vaccination programs. Our findings indicate that the fourth dose among the high-risk group is likely needed by the end of the year.
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Affiliation(s)
- Allison Fisher
- Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA
| | - Hainan Xu
- Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada
| | - Daihai He
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China
| | - Xueying Wang
- Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA
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7
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Mamis K, Farazmand M. Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties. Proc Math Phys Eng Sci 2023. [DOI: 10.1098/rspa.2022.0568] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
Compartmental models are an important quantitative tool in epidemiology, enabling us to forecast the course of a communicable disease. However, the model parameters, such as the infectivity rate of the disease, are riddled with uncertainties, which has motivated the development and use of stochastic compartmental models. Here, we first show that a common stochastic model, which treats the uncertainties as white noise, is fundamentally flawed since it erroneously implies that greater parameter uncertainties will lead to the eradication of the disease. Then, we present a principled modelling of the uncertainties based on reasonable assumptions on the contacts of each individual. Using the central limit theorem and Doob’s theorem on Gaussian Markov processes, we prove that the correlated Ornstein–Uhlenbeck (OU) process is the appropriate tool for modelling uncertainties in the infectivity rate. We demonstrate our results using a compartmental model of the COVID-19 pandemic and the available US data from the Johns Hopkins University COVID-19 database. In particular, we show that the white noise stochastic model systematically underestimates the severity of the Omicron variant of COVID-19, whereas the OU model correctly forecasts the course of this variant. Moreover, using an SIS model of sexually transmitted disease, we derive an exact closed-form solution for the final distribution of infected individuals. This analytical result shows that the white noise model underestimates the severity of the pandemic because of unrealistic noise-induced transitions. Our results strongly support the need for temporal correlations in modelling of uncertainties in compartmental models of infectious disease.
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Affiliation(s)
- Konstantinos Mamis
- Department of Mathematics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27695-8205, USA
| | - Mohammad Farazmand
- Department of Mathematics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27695-8205, USA
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8
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Gourieroux C, Jasiak J. Time varying Markov process with partially observed aggregate data: An application to coronavirus. JOURNAL OF ECONOMETRICS 2023; 232:35-51. [PMID: 33281272 PMCID: PMC7698670 DOI: 10.1016/j.jeconom.2020.09.007] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Revised: 06/08/2020] [Accepted: 09/15/2020] [Indexed: 05/20/2023]
Abstract
A major difficulty in the analysis of Covid-19 transmission is that many infected individuals are asymptomatic. For this reason, the total counts of infected individuals and of recovered immunized individuals are unknown, especially during the early phase of the epidemic. In this paper, we consider a parametric time varying Markov process of Coronavirus transmission and show how to estimate the model parameters and approximate the unobserved counts from daily data on infected and detected individuals and the total daily death counts. This model-based approach is illustrated in an application to French data, performed on April 6, 2020.
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Affiliation(s)
- C Gourieroux
- University of Toronto, Canada, Toulouse School of Economics and CREST, France
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9
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Leitao Á, Vázquez C. The stochastic θ -SEIHRD model: Adding randomness to the COVID-19 spread. COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION 2022; 115:106731. [PMID: 35910551 PMCID: PMC9308140 DOI: 10.1016/j.cnsns.2022.106731] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Revised: 07/14/2022] [Accepted: 07/17/2022] [Indexed: 06/15/2023]
Abstract
In this article we mainly extend a newly introduced deterministic model for the COVID-19 disease to a stochastic setting. More precisely, we incorporated randomness in some coefficients by assuming that they follow a prescribed stochastic dynamics. In this way, the model variables are now represented by stochastic process, that can be simulated by appropriately solving the system of stochastic differential equations. Thus, the model becomes more complete and flexible than the deterministic analogous, as it incorporates additional uncertainties which are present in more realistic situations. In particular, confidence intervals for the main variables and worst case scenarios can be computed.
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Affiliation(s)
- Álvaro Leitao
- CITIC, Universidade da Coruña, Spain
- Department of Mathematics, Universidade da Coruña, Spain
| | - Carlos Vázquez
- CITIC, Universidade da Coruña, Spain
- Department of Mathematics, Universidade da Coruña, Spain
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10
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Brett TS, Rohani P. Containing novel SARS-CoV-2 variants at source is possible with high-intensity sequencing. PNAS NEXUS 2022; 1:pgac159. [PMID: 36111270 PMCID: PMC9465520 DOI: 10.1093/pnasnexus/pgac159] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Accepted: 08/12/2022] [Indexed: 11/16/2022]
Abstract
Throughout the COVID-19 pandemic, control of transmission has been repeatedly thwarted by the emergence of variants of concern (VOC) and their geographic spread. Key questions remain regarding effective means of minimizing the impact of VOC, in particular the feasibility of containing them at source, in light of global interconnectedness. By analysing a stochastic transmission model of COVID-19, we identify the appropriate monitoring requirements that make containment at source feasible. Specifically, precise risk assessment informed primarily by epidemiological indicators (e.g. accumulated hospitalization or mortality reports), is unlikely prior to VOC escape. Consequently, decision makers will need to make containment decisions without confident severity estimates. In contrast, successfully identifying and containing variants via genomic surveillance is realistic, provided sequence processing and dissemination is prompt.
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Affiliation(s)
- Tobias S Brett
- Odum School of Ecology, University of Georgia , Athens, GA 30602, USA
- Center for the Ecology of Infectious Diseases, University of Georgia , Athens, GA 30602, USA
| | - Pejman Rohani
- Odum School of Ecology, University of Georgia , Athens, GA 30602, USA
- Center for the Ecology of Infectious Diseases, University of Georgia , Athens, GA 30602, USA
- Department of Infectious Diseases, College of Veterinary Medicine, University of Georgia , Athens, GA 30602, USA
- Center for Influenza Disease and Emergence Research (CIDER) , Athens, GA 30602, USA
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11
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Andrade J, Duggan J. Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data. PLoS Comput Biol 2022; 18:e1010206. [PMID: 35759506 PMCID: PMC9269962 DOI: 10.1371/journal.pcbi.1010206] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2021] [Revised: 07/08/2022] [Accepted: 05/11/2022] [Indexed: 11/19/2022] Open
Abstract
The effective reproduction number (ℜt) is a theoretical indicator of the course of an infectious disease that allows policymakers to evaluate whether current or previous control efforts have been successful or whether additional interventions are necessary. This metric, however, cannot be directly observed and must be inferred from available data. One approach to obtaining such estimates is fitting compartmental models to incidence data. We can envision these dynamic models as the ensemble of structures that describe the disease's natural history and individuals' behavioural patterns. In the context of the response to the COVID-19 pandemic, the assumption of a constant transmission rate is rendered unrealistic, and it is critical to identify a mathematical formulation that accounts for changes in contact patterns. In this work, we leverage existing approaches to propose three complementary formulations that yield similar estimates for ℜt based on data from Ireland's first COVID-19 wave. We describe these Data Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and DGP2) correspond to stochastic process models whose transmission rate is modelled as Brownian motion processes (Geometric and Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts for incidence and transmission rates, where mobility data is assumed as a proxy of the transmission rate. We perform inference on these structures using Iterated Filtering and the Particle Filter. The final DGP (DGP3) is built from a pool of deterministic models that describe the transmission rate as information delays. We calibrate this pool of models to incidence reports using Hamiltonian Monte Carlo. By following this complementary approach, we assess the tradeoffs associated with each formulation and reflect on the benefits/risks of incorporating proxy data into the inference process. We anticipate this work will help evaluate the implications of choosing a particular formulation for the dynamics and observation of the time-varying transmission rate.
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Affiliation(s)
- Jair Andrade
- Data Science Institute and School of Computer Science, National University of Ireland Galway, Ireland
| | - Jim Duggan
- School of Computer Science, Ryan Institute and Data Science Institute, National University of Ireland Galway, Ireland
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12
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Lin L, Chen B, Zhao Y, Wang W, He D. Two waves of COIVD-19 in Brazilian cities and vaccination impact. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:4657-4671. [PMID: 35430833 DOI: 10.3934/mbe.2022216] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
BACKGROUNDS Brazil has suffered two waves of Coronavirus Disease 2019 (COVID-19). The second wave, coinciding with the spread of the Gamma variant, was more severe than the first wave. Studies have not yet reached a conclusion on some issues including the extent of reinfection, the infection fatality rate (IFR), the infection attack rate (IAR) and the effects of the vaccination campaign in Brazil, though it was reported that confirmed reinfection was at a low level. METHODS We modify the classical Susceptible-Exposed-Infectious-Recovered (SEIR) model with additional class for severe cases, vaccination and time-varying transmission rates. We fit the model to the severe acute respiratory infection (SARI) deaths, which is a proxy of the COVID-19 deaths, in 20 Brazilian cities with the large number of death tolls. We evaluate the vaccination effect by a contrast of "with" vaccination actual scenario and "without" vaccination in a counterfactual scenario. We evaluate the model performance when the reinfection is absent in the model. RESULTS In the 20 Brazilian cities, the model simulated death matched the reported deaths reasonably well. The effect of the vaccination varies across cities. The estimated median IFR is around 1.2%. CONCLUSION Overall, through this modeling exercise, we conclude that the effects of vaccination campaigns vary across cites and the reinfection is not crucial for the second wave. The relatively high IFR could be due to the breakdown of medical system in many cities.
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Affiliation(s)
- Lixin Lin
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong 999077, China
| | - Boqiang Chen
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong 999077, China
| | - Yanji Zhao
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong 999077, China
| | - Weiming Wang
- School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China
| | - Daihai He
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong 999077, China
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13
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Cristancho-Fajardo L, Ezanno P, Vergu E. Dynamic resource allocation for controlling pathogen spread on a large metapopulation network. J R Soc Interface 2022; 19:20210744. [PMID: 35259957 PMCID: PMC8905161 DOI: 10.1098/rsif.2021.0744] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2021] [Accepted: 02/10/2022] [Indexed: 12/03/2022] Open
Abstract
To control the spread of an infectious disease over a large network, the optimal allocation by a social planner of a limited resource is a fundamental and difficult problem. We address this problem for a livestock disease that propagates on an animal trade network according to an epidemiological-demographic model based on animal demographics and trade data. We assume that the resource is dynamically allocated following a certain score, up to the limit of resource availability. We adapt a greedy approach to the metapopulation framework, obtaining new scores that minimize approximations of two different objective functions, for two control measures: vaccination and treatment. Through intensive simulations, we compare the greedy scores with several heuristics. Although topology-based scores can limit the spread of the disease, information on herd health status seems crucial to eradicating the disease. In particular, greedy scores are among the most effective in reducing disease prevalence, even though they do not always perform the best. However, some scores may be preferred in real life because they are easier to calculate or because they use a smaller amount of resources. The developed approach could be adapted to other epidemiological models or to other control measures in the metapopulation setting.
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Affiliation(s)
- Lina Cristancho-Fajardo
- Université Paris-Saclay, INRAE, MaIAGE, Jouy-en-Josas 78350, France
- INRAE, Oniris, BIOEPAR, Site de la Chantrerie, CS40706, Nantes 44307, France
| | - Pauline Ezanno
- INRAE, Oniris, BIOEPAR, Site de la Chantrerie, CS40706, Nantes 44307, France
| | - Elisabeta Vergu
- Université Paris-Saclay, INRAE, MaIAGE, Jouy-en-Josas 78350, France
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14
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Santos-Vega M, Martinez PP, Vaishnav KG, Kohli V, Desai V, Bouma MJ, Pascual M. The neglected role of relative humidity in the interannual variability of urban malaria in Indian cities. Nat Commun 2022; 13:533. [PMID: 35087036 PMCID: PMC8795427 DOI: 10.1038/s41467-022-28145-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Accepted: 01/03/2022] [Indexed: 11/09/2022] Open
Abstract
The rapid pace of urbanization makes it imperative that we better understand the influence of climate forcing on urban malaria transmission. Despite extensive study of temperature effects in vector-borne infections in general, consideration of relative humidity remains limited. With process-based dynamical models informed by almost two decades of monthly surveillance data, we address the role of relative humidity in the interannual variability of epidemic malaria in two semi-arid cities of India. We show a strong and significant effect of humidity during the pre-transmission season on malaria burden in coastal Surat and more arid inland Ahmedabad. Simulations of the climate-driven transmission model with the MLE (Maximum Likelihood Estimates) of the parameters retrospectively capture the observed variability of disease incidence, and also prospectively predict that of 'out-of-fit' cases in more recent years, with high accuracy. Our findings indicate that relative humidity is a critical factor in the spread of urban malaria and potentially other vector-borne epidemics, and that climate change and lack of hydrological planning in cities might jeopardize malaria elimination efforts.
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Affiliation(s)
- M Santos-Vega
- Department of Ecology and Evolution, University of Chicago, Chicago, USA
- Departamento de Ingeniería Biomédica, Grupo de Investigación en Biología Matemática y Computacional BIOMAC, Universidad de los Andes, Bogotá, Colombia
| | - P P Martinez
- Department of Microbiology and Department of Statistics, University of Illinois at Urbana, Champaign, Champaign, IL, USA
| | - K G Vaishnav
- Vector Borne Diseases Control Department, Health Department, Surat Municipal Corporation, Surat, India
| | - V Kohli
- Ahmedabad Municipal Corporation, Ahmedabad, India
| | - V Desai
- Urban Health and Climate Resilience Center of Excellence, (UHCRCE), Surat, India
| | | | - M Pascual
- Department of Ecology and Evolution, University of Chicago, Chicago, USA.
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15
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Elliott S, Gouriéroux C. Estimated reproduction ratios in the SIR model. CAN J STAT 2021; 49:992-1017. [PMID: 34898816 PMCID: PMC8653142 DOI: 10.1002/cjs.11663] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Accepted: 07/27/2021] [Indexed: 12/21/2022]
Abstract
The aim of this article is to understand the extreme variability in estimates of the reproduction ratio R 0 observed in practice. For expository purposes, we consider a discrete-time, stochastic version of the susceptible-infected-recovered model and introduce different approximate maximum likelihood estimators of R 0. We carefully discuss the properties of these estimators and illustrate, by a Monte Carlo study, the widths of confidence intervals for R 0.
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Affiliation(s)
- Sean Elliott
- Department of EconomicsUniversity of TorontoTorontoM5S 2E9OntarioCanada
| | - Christian Gouriéroux
- Department of EconomicsUniversity of TorontoTorontoM5S 2E9OntarioCanada
- Toulouse School of EconomicsToulouse31000France
- Center for Research in Economics and StatisticsPalaiseau91764France
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16
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Arık SÖ, Shor J, Sinha R, Yoon J, Ledsam JR, Le LT, Dusenberry MW, Yoder NC, Popendorf K, Epshteyn A, Euphrosine J, Kanal E, Jones I, Li CL, Luan B, Mckenna J, Menon V, Singh S, Sun M, Ravi AS, Zhang L, Sava D, Cunningham K, Kayama H, Tsai T, Yoneoka D, Nomura S, Miyata H, Pfister T. A prospective evaluation of AI-augmented epidemiology to forecast COVID-19 in the USA and Japan. NPJ Digit Med 2021; 4:146. [PMID: 34625656 PMCID: PMC8501040 DOI: 10.1038/s41746-021-00511-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2021] [Accepted: 08/25/2021] [Indexed: 12/18/2022] Open
Abstract
The COVID-19 pandemic has highlighted the global need for reliable models of disease spread. We propose an AI-augmented forecast modeling framework that provides daily predictions of the expected number of confirmed COVID-19 deaths, cases, and hospitalizations during the following 4 weeks. We present an international, prospective evaluation of our models' performance across all states and counties in the USA and prefectures in Japan. Nationally, incident mean absolute percentage error (MAPE) for predicting COVID-19 associated deaths during prospective deployment remained consistently <8% (US) and <29% (Japan), while cumulative MAPE remained <2% (US) and <10% (Japan). We show that our models perform well even during periods of considerable change in population behavior, and are robust to demographic differences across different geographic locations. We further demonstrate that our framework provides meaningful explanatory insights with the models accurately adapting to local and national policy interventions. Our framework enables counterfactual simulations, which indicate continuing Non-Pharmaceutical Interventions alongside vaccinations is essential for faster recovery from the pandemic, delaying the application of interventions has a detrimental effect, and allow exploration of the consequences of different vaccination strategies. The COVID-19 pandemic remains a global emergency. In the face of substantial challenges ahead, the approach presented here has the potential to inform critical decisions.
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Affiliation(s)
- Sercan Ö Arık
- Google Cloud AI, 1170 Bordeaux Dr, Sunnyvale, CA, USA.
| | - Joel Shor
- Google, Japan, Shibuya, 3-Chrome-21-3, Tokyo, Japan
| | | | - Jinsung Yoon
- Google Cloud AI, 1170 Bordeaux Dr, Sunnyvale, CA, USA
| | | | - Long T Le
- Google Cloud AI, 1170 Bordeaux Dr, Sunnyvale, CA, USA
| | | | | | | | | | | | - Elli Kanal
- Google Cloud AI, 1170 Bordeaux Dr, Sunnyvale, CA, USA
| | - Isaac Jones
- Google Cloud AI, 1170 Bordeaux Dr, Sunnyvale, CA, USA
| | - Chun-Liang Li
- Google Cloud AI, 1170 Bordeaux Dr, Sunnyvale, CA, USA
| | - Beth Luan
- Google, Japan, Shibuya, 3-Chrome-21-3, Tokyo, Japan
| | - Joe Mckenna
- Google Cloud AI, 1170 Bordeaux Dr, Sunnyvale, CA, USA
| | - Vikas Menon
- Google Cloud AI, 1170 Bordeaux Dr, Sunnyvale, CA, USA
| | | | - Mimi Sun
- Google Health, 1600 Amphitheatre Parkway, Mountain View, CA, USA
| | | | - Leyou Zhang
- Google Cloud AI, 1170 Bordeaux Dr, Sunnyvale, CA, USA
| | - Dario Sava
- Google Cloud AI, 1170 Bordeaux Dr, Sunnyvale, CA, USA
| | | | | | - Thomas Tsai
- Harvard School of Public Health, 677 Huntington Ave, Boston, MA, USA
| | - Daisuke Yoneoka
- Department of Health Policy and Management, School of Medicine, Keio University, 35 Shinanomachi, Shinjuku-ku, Tokyo, Japan
- Division of Biostatistics and Bioinformatics, Graduate School of Public Health, St Luke's International University, 3-6-2 Tsukiji, Chuo-ku, Tokyo, Japan
| | - Shuhei Nomura
- Department of Health Policy and Management, School of Medicine, Keio University, 35 Shinanomachi, Shinjuku-ku, Tokyo, Japan
- Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, Japan
| | - Hiroaki Miyata
- Department of Health Policy and Management, School of Medicine, Keio University, 35 Shinanomachi, Shinjuku-ku, Tokyo, Japan
- Department of Healthcare Quality Assessment, Graduate School of Medicine, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, Japan
| | - Tomas Pfister
- Google Cloud AI, 1170 Bordeaux Dr, Sunnyvale, CA, USA
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17
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Zhao S, Lou J, Cao L, Zheng H, Chong MKC, Chen Z, Chan RWY, Zee BCY, Chan PKS, Wang MH. Real-time quantification of the transmission advantage associated with a single mutation in pathogen genomes: a case study on the D614G substitution of SARS-CoV-2. BMC Infect Dis 2021; 21:1039. [PMID: 34620109 PMCID: PMC8495436 DOI: 10.1186/s12879-021-06729-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Accepted: 09/20/2021] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND The COVID-19 pandemic poses serious threats to global health, and the emerging mutation in SARS-CoV-2 genomes, e.g., the D614G substitution, is one of the major challenges of disease control. Characterizing the role of the mutation activities is of importance to understand how the evolution of pathogen shapes the epidemiological outcomes at population scale. METHODS We developed a statistical framework to reconstruct variant-specific reproduction numbers and estimate transmission advantage associated with the mutation activities marked by single substitution empirically. Using likelihood-based approach, the model is exemplified with the COVID-19 surveillance data from January 1 to June 30, 2020 in California, USA. We explore the potential of this framework to generate early warning signals for detecting transmission advantage on a real-time basis. RESULTS The modelling framework in this study links together the mutation activity at molecular scale and COVID-19 transmissibility at population scale. We find a significant transmission advantage of COVID-19 associated with the D614G substitution, which increases the infectivity by 54% (95%CI: 36, 72). For the early alarming potentials, the analytical framework is demonstrated to detect this transmission advantage, before the mutation reaches dominance, on a real-time basis. CONCLUSIONS We reported an evidence of transmission advantage associated with D614G substitution, and highlighted the real-time estimating potentials of modelling framework.
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Affiliation(s)
- Shi Zhao
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
- CUHK Shenzhen Research Institute, Shenzhen, China
| | - Jingzhi Lou
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
| | - Lirong Cao
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
| | - Hong Zheng
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
| | - Marc K. C. Chong
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
- CUHK Shenzhen Research Institute, Shenzhen, China
| | - Zigui Chen
- Department of Microbiology, Chinese University of Hong Kong, Hong Kong, China
| | - Renee W. Y. Chan
- Department of Paediatrics, Chinese University of Hong Kong, Hong Kong, China
- Hong Kong Hub of Pediatric Excellence, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
- CUHK-UMCU Joint Research Laboratory of Respiratory Virus & Immunobiology, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
- Li Ka Shing Institute of Health Sciences, Faculty of Medicine, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
| | - Benny C. Y. Zee
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
- CUHK Shenzhen Research Institute, Shenzhen, China
| | - Paul K. S. Chan
- Department of Microbiology, Chinese University of Hong Kong, Hong Kong, China
| | - Maggie H. Wang
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
- CUHK Shenzhen Research Institute, Shenzhen, China
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18
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Ionides EL, Asfaw K, Park J, King AA. Bagged filters for partially observed interacting systems. J Am Stat Assoc 2021; 118:1078-1089. [PMID: 37333856 PMCID: PMC10274325 DOI: 10.1080/01621459.2021.1974867] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2020] [Revised: 08/17/2021] [Accepted: 08/23/2021] [Indexed: 10/20/2022]
Abstract
Bagging (i.e., bootstrap aggregating) involves combining an ensemble of bootstrap estimators. We consider bagging for inference from noisy or incomplete measurements on a collection of interacting stochastic dynamic systems. Each system is called a unit, and each unit is associated with a spatial location. A motivating example arises in epidemiology, where each unit is a city: the majority of transmission occurs within a city, with smaller yet epidemiologically important interactions arising from disease transmission between cities. Monte Carlo filtering methods used for inference on nonlinear non-Gaussian systems can suffer from a curse of dimensionality as the number of units increases. We introduce bagged filter (BF) methodology which combines an ensemble of Monte Carlo filters, using spatiotemporally localized weights to select successful filters at each unit and time. We obtain conditions under which likelihood evaluation using a BF algorithm can beat a curse of dimensionality, and we demonstrate applicability even when these conditions do not hold. BF can out-perform an ensemble Kalman filter on a coupled population dynamics model describing infectious disease transmission. A block particle filter also performs well on this task, though the bagged filter respects smoothness and conservation laws that a block particle filter can violate.
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Affiliation(s)
| | - Kidus Asfaw
- Department of Statistics, University of Michigan
| | - Joonha Park
- Department of Mathematics, University of Kansas
| | - Aaron A King
- Department of Ecology and Evolutionary Biology & Center for the Study of Complex Systems, University of Michigan
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19
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Martinez AAG, Nääs IDA, de Carvalho-Curi TMR, Abe JM, da Silva Lima ND. A Heuristic and Data Mining Model for Predicting Broiler House Environment Suitability. Animals (Basel) 2021; 11:2780. [PMID: 34679810 PMCID: PMC8532747 DOI: 10.3390/ani11102780] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2021] [Revised: 09/15/2021] [Accepted: 09/17/2021] [Indexed: 11/17/2022] Open
Abstract
The proper combination of environment and flock-based variables plays a critical role in broiler production. However, the housing environment control is mainly focused on temperature monitoring during the broiler growth process. The present study developed a novel predictive model to predict the broiler (Gallus gallus domesticus) rearing conditions' suitability using a data-mining process centered on flock-based and environmental variables. Data were recorded inside four commercial controlled environment broiler houses. The data analysis was conducted in three steps. First, we performed an exploratory and descriptive analysis of the environmental data. In the second step, we labeled the target variable that led to a specific broiler-rearing scenario depending on the age of the birds, the environmental dry-bulb temperature and relative humidity, the ammonia concentration, and the ventilation rate. The output (final rearing condition) was discretized into four categories ('Excellent', 'Good', 'Moderate', and 'Inappropriate'). In the third step, we used the dataset to develop tree models using the data-mining process. The random-tree model only presented accuracy for predicting the 'Excellent' and 'Moderate' rearing conditions. The decision-tree model had high accuracy and indicated that broiler age, relative humidity, and ammonia concentration play a critical role in proper rearing conditions. Using a large amount of data allows the data-mining approach to building up 'if-then' rules that indicate suitable environmental control decision-making by broiler farmers.
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Affiliation(s)
- Angel Antonio Gonzalez Martinez
- Graduate Program in Production Engineering, Universidade Paulista, R. Dr. Bacelar 1212, São Paulo 04026-002, Brazil; (A.A.G.M.); (J.M.A.); (N.D.d.S.L.)
| | - Irenilza de Alencar Nääs
- Graduate Program in Production Engineering, Universidade Paulista, R. Dr. Bacelar 1212, São Paulo 04026-002, Brazil; (A.A.G.M.); (J.M.A.); (N.D.d.S.L.)
| | | | - Jair Minoro Abe
- Graduate Program in Production Engineering, Universidade Paulista, R. Dr. Bacelar 1212, São Paulo 04026-002, Brazil; (A.A.G.M.); (J.M.A.); (N.D.d.S.L.)
| | - Nilsa Duarte da Silva Lima
- Graduate Program in Production Engineering, Universidade Paulista, R. Dr. Bacelar 1212, São Paulo 04026-002, Brazil; (A.A.G.M.); (J.M.A.); (N.D.d.S.L.)
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20
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Jurgens AM, Crutchfield JP. Divergent predictive states: The statistical complexity dimension of stationary, ergodic hidden Markov processes. CHAOS (WOODBURY, N.Y.) 2021; 31:083114. [PMID: 34470245 DOI: 10.1063/5.0050460] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 07/04/2021] [Indexed: 06/13/2023]
Abstract
Even simply defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains, the consequences are dramatic. Their predictive models are generically infinite state. Until recently, one could determine neither their intrinsic randomness nor structural complexity. The prequel to this work introduced methods to accurately calculate the Shannon entropy rate (randomness) and to constructively determine their minimal (though, infinite) set of predictive features. Leveraging this, we address the complementary challenge of determining how structured hidden Markov processes are by calculating their statistical complexity dimension-the information dimension of the minimal set of predictive features. This tracks the divergence rate of the minimal memory resources required to optimally predict a broad class of truly complex processes.
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Affiliation(s)
- Alexandra M Jurgens
- Complexity Sciences Center, Physics and Astronomy Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
| | - James P Crutchfield
- Complexity Sciences Center, Physics and Astronomy Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA
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21
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Horn AL, Jiang L, Washburn F, Hvitfeldt E, de la Haye K, Nicholas W, Simon P, Pentz M, Cozen W, Sood N, Conti DV. An integrated risk and epidemiological model to estimate risk-stratified COVID-19 outcomes for Los Angeles County: March 1, 2020-March 1, 2021. PLoS One 2021; 16:e0253549. [PMID: 34166416 PMCID: PMC8224896 DOI: 10.1371/journal.pone.0253549] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2021] [Accepted: 06/07/2021] [Indexed: 01/08/2023] Open
Abstract
The objective of this study was to use available data on the prevalence of COVID-19 risk factors in subpopulations and epidemic dynamics at the population level to estimate probabilities of severe illness and the case and infection fatality rates (CFR and IFR) stratified across subgroups representing all combinations of the risk factors age, comorbidities, obesity, and smoking status. We focus on the first year of the epidemic in Los Angeles County (LAC) (March 1, 2020-March 1, 2021), spanning three epidemic waves. A relative risk modeling approach was developed to estimate conditional effects from available marginal data. A dynamic stochastic epidemic model was developed to produce time-varying population estimates of epidemic parameters including the transmission and infection observation rate. The epidemic and risk models were integrated to produce estimates of subpopulation-stratified probabilities of disease progression and CFR and IFR for LAC. The probabilities of disease progression and CFR and IFR were found to vary as extensively between age groups as within age categories combined with the presence of absence of other risk factors, suggesting that it is inappropriate to summarize epidemiological parameters for age categories alone, let alone the entire population. The fine-grained subpopulation-stratified estimates of COVID-19 outcomes produced in this study are useful in understanding disparities in the effect of the epidemic on different groups in LAC, and can inform analyses of targeted subpopulation-level policy interventions.
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Affiliation(s)
- Abigail L. Horn
- Department of Preventive Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States of America
| | - Lai Jiang
- Department of Preventive Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States of America
| | - Faith Washburn
- Los Angeles County Department of Public Health, Los Angeles, CA, United States of America
| | - Emil Hvitfeldt
- Department of Preventive Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States of America
| | - Kayla de la Haye
- Department of Preventive Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States of America
| | - William Nicholas
- Los Angeles County Department of Public Health, Los Angeles, CA, United States of America
| | - Paul Simon
- Los Angeles County Department of Public Health, Los Angeles, CA, United States of America
| | - Maryann Pentz
- Department of Preventive Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States of America
| | - Wendy Cozen
- Department of Preventive Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States of America
| | - Neeraj Sood
- Sol Price School of Public Policy, University of Southern California, Los Angeles, CA, United States of America
- Schaeffer Center for Health Policy and Economics, University of Southern California, Los Angeles, CA, United States of America
| | - David V. Conti
- Department of Preventive Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA, United States of America
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22
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Stocks T, Britton T, Höhle M. Model selection and parameter estimation for dynamic epidemic models via iterated filtering: application to rotavirus in Germany. Biostatistics 2021; 21:400-416. [PMID: 30265310 PMCID: PMC7307980 DOI: 10.1093/biostatistics/kxy057] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Revised: 05/27/2018] [Accepted: 07/14/2018] [Indexed: 01/01/2023] Open
Abstract
Despite the wide application of dynamic models in infectious disease epidemiology, the particular modeling of variability in the different model components is often subjective rather than the result of a thorough model selection process. This is in part because inference for a stochastic transmission model can be difficult since the likelihood is often intractable due to partial observability. In this work, we address the question of adequate inclusion of variability by demonstrating a systematic approach for model selection and parameter inference for dynamic epidemic models. For this, we perform inference for six partially observed Markov process models, which assume the same underlying transmission dynamics, but differ with respect to the amount of variability they allow for. The inference framework for the stochastic transmission models is provided by iterated filtering methods, which are readily implemented in the R package pomp by King and others (2016, Statistical inference for partially observed Markov processes via the R package pomp. Journal of Statistical Software69, 1–43). We illustrate our approach on German rotavirus surveillance data from 2001 to 2008, discuss practical difficulties of the methods used and calculate a model based estimate for the basic reproduction number \documentclass[12pt]{minimal}
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}{}$R_0$\end{document} using these data.
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Affiliation(s)
- Theresa Stocks
- Department of Mathematics, Stockholm University, 10691 Stockholm, Sweden
| | - Tom Britton
- Department of Mathematics, Stockholm University, 10691 Stockholm, Sweden
| | - Michael Höhle
- Department of Mathematics, Stockholm University, 10691 Stockholm, Sweden
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23
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Accounting for farmers' control decisions in a model of pathogen spread through animal trade. Sci Rep 2021; 11:9581. [PMID: 33953245 PMCID: PMC8100180 DOI: 10.1038/s41598-021-88471-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2020] [Accepted: 04/12/2021] [Indexed: 02/03/2023] Open
Abstract
Accounting for individual decisions in mechanistic epidemiological models remains a challenge, especially for unregulated endemic animal diseases for which control is not compulsory. We propose a new integrative model by combining two sub-models. The first one for the dynamics of a livestock epidemic on a metapopulation network, grounded on demographic and animal trade data. The second one for farmers' behavior regarding the adoption of a control measure against the disease spread in their herd. The measure is specified as a protective vaccine with given economic implications, and the model is numerically studied through intensive simulations and sensitivity analyses. While each tested parameter of the model has an impact on the overall model behavior, the most important factor in farmers' decisions is their frequency, as this factor explained almost 30% of the variation in decision-related outputs of the model. Indeed, updating frequently local health information impacts positively vaccination, and limits strongly the propagation of the pathogen. Our study is relevant for the understanding of the interplay between decision-related human behavior and livestock epidemic dynamics. The model can be used for other structures of epidemic models or different interventions, by adapting its components.
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24
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Baccini M, Cereda G, Viscardi C. The first wave of the SARS-CoV-2 epidemic in Tuscany (Italy): A SI2R2D compartmental model with uncertainty evaluation. PLoS One 2021; 16:e0250029. [PMID: 33882085 PMCID: PMC8059849 DOI: 10.1371/journal.pone.0250029] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Accepted: 03/29/2021] [Indexed: 01/10/2023] Open
Abstract
With the aim of studying the spread of the SARS-CoV-2 infection in the Tuscany region of Italy during the first epidemic wave (February-June 2020), we define a compartmental model that accounts for both detected and undetected infections and assumes that only notified cases can die. We estimate the infection fatality rate, the case fatality rate, and the basic reproduction number, modeled as a time-varying function, by calibrating on the cumulative daily number of observed deaths and notified infected, after fixing to plausible values the other model parameters to assure identifiability. The confidence intervals are estimated by a parametric bootstrap procedure and a Global Sensitivity Analysis is performed to assess the sensitivity of the estimates to changes in the values of the fixed parameters. According to our results, the basic reproduction number drops from an initial value of 6.055 to 0 at the end of the national lockdown, then it grows again, but remaining under 1. At the beginning of the epidemic, the case and the infection fatality rates are estimated to be 13.1% and 2.3%, respectively. Among the parameters considered as fixed, the average time from infection to recovery for the not notified infected appears to be the most impacting one on the model estimates. The probability for an infected to be notified has a relevant impact on the infection fatality rate and on the shape of the epidemic curve. This stresses the need of collecting information on these parameters to better understand the phenomenon and get reliable predictions.
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Affiliation(s)
- Michela Baccini
- Department of Statistics, Computer Science, Applications (DiSIA), University of Florence, Florence, Italy
| | - Giulia Cereda
- Department of Statistics, Computer Science, Applications (DiSIA), University of Florence, Florence, Italy
| | - Cecilia Viscardi
- Department of Statistics, Computer Science, Applications (DiSIA), University of Florence, Florence, Italy
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25
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Zhao S, Lou J, Chong MKC, Cao L, Zheng H, Chen Z, Chan RWY, Zee BCY, Chan PKS, Wang MH. Inferring the Association between the Risk of COVID-19 Case Fatality and N501Y Substitution in SARS-CoV-2. Viruses 2021; 13:638. [PMID: 33918060 PMCID: PMC8070306 DOI: 10.3390/v13040638] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Revised: 04/05/2021] [Accepted: 04/06/2021] [Indexed: 02/07/2023] Open
Abstract
As COVID-19 is posing a serious threat to global health, the emerging mutation in SARS-CoV-2 genomes, for example, N501Y substitution, is one of the major challenges against control of the pandemic. Characterizing the relationship between mutation activities and the risk of severe clinical outcomes is of public health importance for informing the healthcare decision-making process. Using a likelihood-based approach, we developed a statistical framework to reconstruct a time-varying and variant-specific case fatality ratio (CFR), and to estimate changes in CFR associated with a single mutation empirically. For illustration, the statistical framework is implemented to the COVID-19 surveillance data in the United Kingdom (UK). The reconstructed instantaneous CFR gradually increased from 1.0% in September to 2.2% in November 2020 and stabilized at this level thereafter, which monitors the mortality risk of COVID-19 on a real-time basis. We identified a link between the SARS-CoV-2 mutation activity at molecular scale and COVID-19 mortality risk at population scale, and found that the 501Y variants may slightly but not significantly increase 18% of fatality risk than the preceding 501N variants. We found no statistically significant evidence of change in COVID-19 mortality risk associated with 501Y variants, and highlighted the real-time estimating potentials of the modelling framework.
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Affiliation(s)
- Shi Zhao
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China; (J.L.); (M.K.C.C.); (L.C.); (H.Z.); (B.C.Y.Z.)
- CUHK Shenzhen Research Institute, Shenzhen 518000, China
| | - Jingzhi Lou
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China; (J.L.); (M.K.C.C.); (L.C.); (H.Z.); (B.C.Y.Z.)
| | - Marc K. C. Chong
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China; (J.L.); (M.K.C.C.); (L.C.); (H.Z.); (B.C.Y.Z.)
- CUHK Shenzhen Research Institute, Shenzhen 518000, China
| | - Lirong Cao
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China; (J.L.); (M.K.C.C.); (L.C.); (H.Z.); (B.C.Y.Z.)
- CUHK Shenzhen Research Institute, Shenzhen 518000, China
| | - Hong Zheng
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China; (J.L.); (M.K.C.C.); (L.C.); (H.Z.); (B.C.Y.Z.)
| | - Zigui Chen
- Department of Microbiology, Chinese University of Hong Kong, Hong Kong, China; (Z.C.); (P.K.S.C.)
| | - Renee W. Y. Chan
- Department of Pediatrics, Chinese University of Hong Kong, Hong Kong, China;
- Hong Kong Hub of Pediatric Excellence, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
- CUHK-UMCU Joint Research Laboratory of Respiratory Virus & Immunobiology, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
- Li Ka Shing Institute of Health Sciences, Faculty of Medicine, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China
| | - Benny C. Y. Zee
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China; (J.L.); (M.K.C.C.); (L.C.); (H.Z.); (B.C.Y.Z.)
- CUHK Shenzhen Research Institute, Shenzhen 518000, China
| | - Paul K. S. Chan
- Department of Microbiology, Chinese University of Hong Kong, Hong Kong, China; (Z.C.); (P.K.S.C.)
| | - Maggie H. Wang
- JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China; (J.L.); (M.K.C.C.); (L.C.); (H.Z.); (B.C.Y.Z.)
- CUHK Shenzhen Research Institute, Shenzhen 518000, China
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26
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Pacheco PMCL, Savi MA, Savi PV. COVID-19 dynamics considering the influence of hospital infrastructure: an investigation into Brazilian scenarios. NONLINEAR DYNAMICS 2021; 106:1325-1346. [PMID: 33746362 PMCID: PMC7955701 DOI: 10.1007/s11071-021-06323-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2020] [Accepted: 02/22/2021] [Indexed: 05/24/2023]
Abstract
COVID-19 dynamics is one of the most relevant subjects nowadays, and, in this regard, mathematical modeling and numerical simulations are of special interest. This paper describes COVID-19 dynamics based on a novel version of the susceptible-exposed-infectious-removed model. Removed population is split into recovered and death populations allowing a better comprehension of real situations. Besides, the total population is reduced based on the number of deaths. Hospital infrastructure is also included into the mathematical description allowing the consideration of collapse scenarios. Initially, a model verification is carried out calibrating system parameters with data from China outbreak that is considered a benchmark due the availability of data for the entire cycle. Afterward, Brazil outbreak is of concern, calibrating the model and developing numerical simulations. Results show several scenarios highlighting the importance of social isolation and hospital infrastructure. System dynamics has a strong sensitivity to transmission rate showing the importance of numerical simulations to guide public health decision strategies. Results also show that complex dynamical responses can emerge due to the oscillations of the transmission rate, being associated with distinct infection subsequent waves.
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Affiliation(s)
- Pedro M. C. L. Pacheco
- Department of Mechanical Engineering, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca - CEFET/RJ, Rio de Janeiro, 20.271.110 Brazil
| | - Marcelo A. Savi
- Center for Nonlinear Mechanics, COPPE – Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, P.O. Box 68.503, Rio de Janeiro, RJ 21.941.972 Brazil
| | - Pedro V. Savi
- Center for Nonlinear Mechanics, COPPE – Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, P.O. Box 68.503, Rio de Janeiro, RJ 21.941.972 Brazil
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Horn AL, Jiang L, Washburn F, Hvitfeldt E, de la Haye K, Nicholas W, Simon P, Pentz M, Cozen W, Sood N, Conti DV. Estimation of COVID-19 risk-stratified epidemiological parameters and policy implications for Los Angeles County through an integrated risk and stochastic epidemiological model. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2020:2020.12.11.20209627. [PMID: 33367291 PMCID: PMC7756248 DOI: 10.1101/2020.12.11.20209627] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
Background Health disparities have emerged with the COVID-19 epidemic because the risk of exposure to infection and the prevalence of risk factors for severe outcomes given infection vary within and between populations. However, estimated epidemic quantities such as rates of severe illness and death, the case fatality rate (CFR), and infection fatality rate (IFR), are often expressed in terms of aggregated population-level estimates due to the lack of epidemiological data at the refined subpopulation level. For public health policy makers to better address the pandemic, stratified estimates are necessary to investigate the potential outcomes of policy scenarios targeting specific subpopulations. Methods We develop a framework for using available data on the prevalence of COVID-19 risk factors (age, comorbidities, BMI, smoking status) in subpopulations, and epidemic dynamics at the population level and stratified by age, to estimate subpopulation-stratified probabilities of severe illness and the CFR (as deaths over observed infections) and IFR (as deaths over estimated total infections) across risk profiles representing all combinations of risk factors including age, comorbidities, obesity class, and smoking status. A dynamic epidemic model is integrated with a relative risk model to produce time-varying subpopulation-stratified estimates. The integrated model is used to analyze dynamic outcomes and parameters by population and subpopulation, and to simulate alternate policy scenarios that protect specific at-risk subpopulations or modify the population-wide transmission rate. The model is calibrated to data from the Los Angeles County population during the period March 1 - October 15 2020. Findings We estimate a rate of 0.23 (95% CI: 0.13,0.33) of infections observed before April 15, which increased over the epidemic course to 0.41 (0.11,0.69). Overall population-average IFR( t ) estimates for LAC peaked at 0.77% (0.38%,1.15%) on May 15 and decreased to 0.55% (0.24%,0.90%) by October 15. The population-average IFR( t ) stratified by age group varied extensively across subprofiles representing each combination of the additional risk factors considered (comorbidities, BMI, smoking). We found median IFRs ranging from 0.009%-0.04% in the youngest age group (0-19), from 0.1%-1.8% for those aged 20-44, 0.36%-4.3% for those aged 45-64, and 1.02%-5.42% for those aged 65+. In the group aged 65+ for which the rate of unobserved infections is likely much lower, we find median CFRs in the range 4.4%-23.45%. The initial societal lockdown period avoided overwhelming healthcare capacity and greatly reduced the observed death count. In comparative scenario analysis, alternative policies in which the population-wide transmission rate is reduced to a moderate and sustainable level of non-pharmaceutical interventions (NPIs) would not have been sufficient to avoid overwhelming healthcare capacity, and additionally would have exceeded the observed death count. Combining the moderate NPI policy with stringent protection of the at-risk subpopulation of individuals 65+ would have resulted in a death count similar to observed levels, but hospital counts would have approached capacity limits. Interpretation The risk of severe illness and death of COVID-19 varies tremendously across subpopulations and over time, suggesting that it is inappropriate to summarize epidemiological parameters for the entire population and epidemic time period. This includes variation not only across age groups, but also within age categories combined with other risk factors analyzed in this study (comorbidities, obesity status, smoking). In the policy analysis accounting for differences in IFR across risk groups in comparing the control of infections and protection of higher risk groups, we find that the strict initial lockdown period in LAC was effective because it both reduced overall transmission and protected individuals at greater risk, resulting in preventing both healthcare overload and deaths. While similar numbers of deaths as observed in LAC could have been achieved with a more moderate NPI policy combined with greater protection of individuals 65+, this would have come at the expense of overwhelming the healthcare system. In anticipation of a continued rise in cases in LAC this winter, policy makers need to consider the trade offs of various policy options on the numbers of the overall population that may become infected, severely ill, and that die when considering policies targeted at subpopulations at greatest risk of transmitting infection and at greatest risk for developing severe outcomes.
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Krylova O, Earn DJD. Patterns of smallpox mortality in London, England, over three centuries. PLoS Biol 2020; 18:e3000506. [PMID: 33347440 PMCID: PMC7751884 DOI: 10.1371/journal.pbio.3000506] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2019] [Accepted: 11/17/2020] [Indexed: 11/19/2022] Open
Abstract
Smallpox is unique among infectious diseases in the degree to which it devastated human populations, its long history of control interventions, and the fact that it has been successfully eradicated. Mortality from smallpox in London, England was carefully documented, weekly, for nearly 300 years, providing a rare and valuable source for the study of ecology and evolution of infectious disease. We describe and analyze smallpox mortality in London from 1664 to 1930. We digitized the weekly records published in the London Bills of Mortality (LBoM) and the Registrar General's Weekly Returns (RGWRs). We annotated the resulting time series with a sequence of historical events that might have influenced smallpox dynamics in London. We present a spectral analysis that reveals how periodicities in reported smallpox mortality changed over decades and centuries; many of these changes in epidemic patterns are correlated with changes in control interventions and public health policies. We also examine how the seasonality of reported smallpox mortality changed from the 17th to 20th centuries in London.
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Affiliation(s)
- Olga Krylova
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
| | - David J. D. Earn
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
- M.G. DeGroote Institute for Infectious Disease Research, McMaster University, Hamilton, Ontario, Canada
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A Mathematical Description of the Dynamics of Coronavirus Disease 2019 (COVID-19): A Case Study of Brazil. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2020; 2020:9017157. [PMID: 33029196 PMCID: PMC7528041 DOI: 10.1155/2020/9017157] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/28/2020] [Accepted: 08/03/2020] [Indexed: 02/06/2023]
Abstract
This paper deals with the mathematical modeling and numerical simulations related to the coronavirus dynamics. A description is developed based on the framework of the susceptible-exposed-infectious-removed model. Initially, a model verification is carried out calibrating system parameters with data from China, Italy, Iran, and Brazil. Results show the model capability to predict infectious evolution. Afterward, numerical simulations are performed in order to analyze different scenarios of COVID-19 in Brazil. Results show the importance of the governmental and individual actions to control the number and the period of the critical situations related to the pandemic.
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Park J, Ionides EL. Inference on high-dimensional implicit dynamic models using a guided intermediate resampling filter. STATISTICS AND COMPUTING 2020; 30:1497-1522. [PMID: 35664372 PMCID: PMC9164307 DOI: 10.1007/s11222-020-09957-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2019] [Accepted: 06/04/2020] [Indexed: 06/15/2023]
Abstract
We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition densities arise in models defined implicitly by simulation algorithms. Widely used particle filter methods are applicable to nonlinear, non-Gaussian models but suffer from the curse of dimensionality. Improved scalability is provided by ensemble Kalman filter methods, but these are inappropriate for highly nonlinear and non-Gaussian models. We propose a particle filter method having improved practical and theoretical scalability with respect to the model dimension. This method is applicable to implicitly defined models having analytically intractable transition densities. Our method is developed based on the assumption that the latent process is defined in continuous time and that a simulator of this latent process is available. In this method, particles are propagated at intermediate time intervals between observations and are resampled based on a forecast likelihood of future observations. We combine this particle filter with parameter estimation methodology to enable likelihood-based inference for highly nonlinear spatiotemporal systems. We demonstrate our methodology on a stochastic Lorenz 96 model and a model for the population dynamics of infectious diseases in a network of linked regions.
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Modeling the 2014-2015 Ebola Virus Disease Outbreaks in Sierra Leone, Guinea, and Liberia with Effect of High- and Low-risk Susceptible Individuals. Bull Math Biol 2020; 82:102. [PMID: 32734342 DOI: 10.1007/s11538-020-00779-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2019] [Accepted: 07/14/2020] [Indexed: 10/23/2022]
Abstract
Ebola virus disease (EVD) is a rare but fatal disease of humans and other primates caused by Ebola viruses. Study shows that the 2014-2015 EVD outbreak causes more than 10,000 deaths. In this paper, we propose and analyze a deterministic model to study the transmission dynamics of EVD in Sierra Leone, Guinea, and Liberia. Our analyses show that the model has two equilibria: (1) the disease-free equilibrium (DFE) which is locally asymptotically stable when the basic reproduction number ([Formula: see text]) is less than unity and unstable if it is greater than one, and (2) an endemic equilibrium (EE) which is globally asymptotically stable when [Formula: see text] is greater than unity. Furthermore, the backward bifurcation occurs, a coexistence between a stale DFE and a stable EE even if the [Formula: see text] is less than unity, which makes the disease control more strenuous and would depend on the initial size of subpopulation. By fitting to reported Ebola cases from Sierra Leone, Guinea, and Liberia in 2014-2015, our model has captured the epidemic patterns in all three countries and shed light on future Ebola control and prevention strategies.
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He D, Zhao S, Lin Q, Musa SS, Stone L. New estimates of the Zika virus epidemic attack rate in Northeastern Brazil from 2015 to 2016: A modelling analysis based on Guillain-Barré Syndrome (GBS) surveillance data. PLoS Negl Trop Dis 2020; 14:e0007502. [PMID: 32348302 PMCID: PMC7213748 DOI: 10.1371/journal.pntd.0007502] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2019] [Revised: 05/11/2020] [Accepted: 03/16/2020] [Indexed: 12/13/2022] Open
Abstract
BACKGROUND Between January 2015 and August 2016, two epidemic waves of Zika virus (ZIKV) disease swept the Northeastern (NE) region of Brazil. As a result, two waves of Guillain-Barré Syndrome (GBS) were observed concurrently. The mandatory reporting of ZIKV disease began region-wide in February 2016, and it is believed that ZIKV cases were significantly under-reported before that. The changing reporting rate has made it difficult to estimate the ZIKV infection attack rate, and studies in the literature vary widely from 17% to > 50%. The same applies to other key epidemiological parameters. In contrast, the diagnosis and reporting of GBS cases were reasonably reliable given the severity and easy recognition of the disease symptoms. In this paper, we aim to estimate the real number of ZIKV cases (i.e., the infection attack rate) and their dynamics in time, by scaling up from GBS surveillance data in NE Brazil. METHODOLOGY A mathematical compartmental model is constructed that makes it possible to infer the true epidemic dynamics of ZIKV cases based on surveillance data of excess GBS cases. The model includes the possibility that asymptomatic ZIKV cases are infectious. The model is fitted to the GBS surveillance data and the key epidemiological parameters are inferred by using a plug-and-play likelihood-based estimation. We make use of regional weather data to determine possible climate-driven impacts on the reproductive number [Formula: see text], and to infer the true ZIKV epidemic dynamics. FINDINGS AND CONCLUSIONS The GBS surveillance data can be used to study ZIKV epidemics and may be appropriate when ZIKV reporting rates are not well understood. The overall infection attack rate (IAR) of ZIKV is estimated to be 24.1% (95% confidence interval: 17.1%-29.3%) of the population. By examining various asymptomatic scenarios, the IAR is likely to be lower than 33% over the two ZIKV waves. The risk rate from symptomatic ZIKV infection to develop GBS was estimated as ρ = 0.0061% (95% CI: 0.0050%-0.0086%) which is significantly less than current estimates. We found a positive association between local temperature and the basic reproduction number, [Formula: see text]. Our analysis revealed that asymptomatic infections affect the estimation of ZIKV epidemics and need to also be carefully considered in related modelling studies. According to the estimated effective reproduction number and population wide susceptibility, we comment that a ZIKV outbreak would be unlikely in NE Brazil in the near future.
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Affiliation(s)
- Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Shi Zhao
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
- Division of Biostatistics, JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
- Clinical Trials and Biostatistics Lab, Shenzhen Research Institute, Chinese University of Hong Kong, Shenzhen, China
| | - Qianying Lin
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
- Michigan Institute for Data Science, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Salihu S. Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Lewi Stone
- Mathematical Science, School of Science, RMIT University, Melbourne, Victoria, Australia
- Biomathematics Unit, School of Zoology, Faculty of Life Sciences, Tel Aviv University, Tel Aviv, Israel
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A Note on Observation Processes in Epidemic Models. Bull Math Biol 2020; 82:37. [PMID: 32146583 DOI: 10.1007/s11538-020-00713-2] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2019] [Accepted: 02/24/2020] [Indexed: 10/24/2022]
Abstract
Many disease models focus on characterizing the underlying transmission mechanism but make simple, possibly naive assumptions about how infections are reported. In this note, we use a simple deterministic Susceptible-Infected-Removed (SIR) model to compare two common assumptions about disease incidence reports: Individuals can report their infection as soon as they become infected or as soon as they recover. We show that incorrect assumptions about the underlying observation processes can bias estimates of the basic reproduction number and lead to overly narrow confidence intervals.
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Zhao S, Musa SS, Hebert JT, Cao P, Ran J, Meng J, He D, Qin J. Modelling the effective reproduction number of vector-borne diseases: the yellow fever outbreak in Luanda, Angola 2015-2016 as an example. PeerJ 2020; 8:e8601. [PMID: 32149023 PMCID: PMC7049463 DOI: 10.7717/peerj.8601] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2019] [Accepted: 01/19/2020] [Indexed: 01/02/2023] Open
Abstract
The burden of vector-borne diseases (Dengue, Zika virus, yellow fever, etc.) gradually increased in the past decade across the globe. Mathematical modelling on infectious diseases helps to study the transmission dynamics of the pathogens. Theoretically, the diseases can be controlled and eventually eradicated by maintaining the effective reproduction number, (R eff ), strictly less than 1. We established a vector-host compartmental model, and derived (R eff ) for vector-borne diseases. The analytic form of the (R eff ) was found to be the product of the basic reproduction number and the geometric average of the susceptibilities of the host and vector populations. The (R eff ) formula was demonstrated to be consistent with the estimates of the 2015-2016 yellow fever outbreak in Luanda, and distinguished the second minor epidemic wave. For those using the compartmental model to study the vector-borne infectious disease epidemics, we further remark that it is important to be aware of whether one or two generations is considered for the transition "from host to vector to host" in reproduction number calculation.
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Affiliation(s)
- Shi Zhao
- School of Nursing, Hong Kong Polytechnic University, Hong Kong, China
- Division of Biostatistics, JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
- Clinical Trials and Biostatistics Lab, Shenzhen Research Institute, Chinese University of Hong Kong, Shenzhen, China
| | - Salihu S. Musa
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Jay T. Hebert
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Peihua Cao
- Department of Hepatobiliary Surgery II, Zhujiang Hospital, Southern Medical University, Guangzhou, China
| | - Jinjun Ran
- School of Public Health, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong, China
| | - Jiayi Meng
- School of Economics and Finance, Xi’an International Studies University, Xi’an, China
| | - Daihai He
- Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
| | - Jing Qin
- School of Nursing, Hong Kong Polytechnic University, Hong Kong, China
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Musa SS, Zhao S, Gao D, Lin Q, Chowell G, He D. Mechanistic modelling of the large-scale Lassa fever epidemics in Nigeria from 2016 to 2019. J Theor Biol 2020; 493:110209. [PMID: 32097608 DOI: 10.1016/j.jtbi.2020.110209] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2019] [Revised: 02/15/2020] [Accepted: 02/19/2020] [Indexed: 01/22/2023]
Abstract
Lassa fever, also known as Lassa hemorrhagic fever, is a virus that has generated recurrent outbreaks in West Africa. We use mechanistic modelling to study the Lassa fever epidemics in Nigeria from 2016-19. Our model describes the interaction between human and rodent populations with the consideration of quarantine, isolation and hospitalization processes. Our model supports the phenomenon of forward bifurcation where the stability between disease-free equilibrium and endemic equilibrium exchanges. Moreover, our model captures well the incidence curves from surveillance data. In particular, our model is able to reconstruct the periodic rodent and human forces of infection. Furthermore, we suggest that the three major epidemics from 2016-19 can be modelled by properly characterizing the rodent (or human) force of infection while the estimated human force of infection also present similar patterns across outbreaks. Our results suggest that the initial susceptibility likely increased across the three outbreaks from 2016-19. Our results highlight the similarity of the transmission dynamics driving three major Lassa fever outbreaks in the endemic areas.
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Affiliation(s)
- Salihu S Musa
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong; Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria
| | - Shi Zhao
- School of Nursing, The Hong Kong Polytechnic University, Hong Kong; JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong; Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China
| | - Daozhou Gao
- Mathematics and Science College, Shanghai Normal University, Shanghai, China
| | - Qianying Lin
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong; Michigan Institute for Data Science, University of Michigan, Ann Arbor, MI, USA
| | - Gerardo Chowell
- School of Public Health, Georgia State University, Atlanta, GA, USA; Fogarty International Center, National Institute of Health, Bethesda, MD, USA
| | - Daihai He
- Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong.
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Ganyani T, Faes C, Hens N. Inference of the generalized-growth model via maximum likelihood estimation: A reflection on the impact of overdispersion. J Theor Biol 2019; 484:110029. [PMID: 31568788 DOI: 10.1016/j.jtbi.2019.110029] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Revised: 07/15/2019] [Accepted: 09/26/2019] [Indexed: 01/17/2023]
Abstract
Recently, the generalized-growth model was introduced as a flexible approach to characterize growth dynamics of disease outbreaks during the early ascending phase. In this work, by using classical maximum likelihood estimation to obtain parameter estimates, we evaluate the impact of varying levels of overdispersion on the inference of the growth scaling parameter through comparing Poisson and Negative binomial models. In particular, under exponential and sub-exponential growth scenarios, we evaluate, via simulations, the error rate of making an incorrect characterization of early outbreak growth patterns. Simulation results show that the ability to correctly identify early outbreak growth patterns can be affected by overdispersion even when accounted for using the Negative binomial model. We exemplify our findings using data on five different outbreaks. Overall, our results show that estimates should be interpreted with caution when data are overdispersed.
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Affiliation(s)
- Tapiwa Ganyani
- Interuniversity Institute for Biostatistics and statistical Bioinformatics, UHasselt (Hasselt University), Diepenbeek, Belgium.
| | - Christel Faes
- Interuniversity Institute for Biostatistics and statistical Bioinformatics, UHasselt (Hasselt University), Diepenbeek, Belgium
| | - Niel Hens
- Interuniversity Institute for Biostatistics and statistical Bioinformatics, UHasselt (Hasselt University), Diepenbeek, Belgium; Centre for Health Economics Research and Modelling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
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O'Dea EB, Park AW, Drake JM. Estimating the distance to an epidemic threshold. J R Soc Interface 2019; 15:rsif.2018.0034. [PMID: 29950512 PMCID: PMC6030631 DOI: 10.1098/rsif.2018.0034] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2018] [Accepted: 05/31/2018] [Indexed: 12/20/2022] Open
Abstract
The epidemic threshold of the susceptible-infected-recovered model is a boundary separating parameters that permit epidemics from those that do not. This threshold corresponds to parameters where the system's equilibrium becomes unstable. Consequently, we use the average rate at which deviations from the equilibrium shrink to define a distance to this threshold. However, the vital dynamics of the host population may occur slowly even when transmission is far from threshold levels. Here, we show analytically how such slow dynamics can prevent estimation of the distance to the threshold from fluctuations in the susceptible population. Although these results are exact only in the limit of long-term observation of a large system, simulations show that they still provide useful insight into systems with a range of population sizes, environmental noise and observation schemes. Having established some guidelines about when estimates are accurate, we then illustrate how multiple distance estimates can be used to estimate the rate of approach to the threshold. The estimation approach is general and may be applicable to zoonotic pathogens such as Middle East respiratory syndrome-related coronavirus (MERS-CoV) as well as vaccine-preventable diseases like measles.
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Affiliation(s)
- Eamon B O'Dea
- Department of Ecology, College of Veterinary Medicine, University of Georgia, Athens, GA, USA .,Center for the Ecology of Infectious Diseases, College of Veterinary Medicine, University of Georgia, Athens, GA, USA
| | - Andrew W Park
- Odum School of Ecology, College of Veterinary Medicine, University of Georgia, Athens, GA, USA.,Infectious Diseases, College of Veterinary Medicine, University of Georgia, Athens, GA, USA
| | - John M Drake
- Center for the Ecology of Infectious Diseases, College of Veterinary Medicine, University of Georgia, Athens, GA, USA.,Odum School of Ecology, College of Veterinary Medicine, University of Georgia, Athens, GA, USA
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Marino JA, Peacor SD, Bunnell DB, Vanderploeg HA, Pothoven SA, Elgin AK, Bence JR, Jiao J, Ionides EL. Evaluating consumptive and nonconsumptive predator effects on prey density using field time-series data. Ecology 2019; 100:e02583. [PMID: 30565223 DOI: 10.1002/ecy.2583] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/07/2018] [Accepted: 11/13/2018] [Indexed: 12/30/2022]
Abstract
Determining the degree to which predation affects prey abundance in natural communities constitutes a key goal of ecological research. Predators can affect prey through both consumptive effects (CEs) and nonconsumptive effects (NCEs), although the contributions of each mechanism to the density of prey populations remain largely hypothetical in most systems. Common statistical methods applied to time-series data cannot elucidate the mechanisms responsible for hypothesized predator effects on prey density (e.g., differentiate CEs from NCEs), nor can they provide parameters for predictive models. State-space models (SSMs) applied to time-series data offer a way to meet these goals. Here, we employ SSMs to assess effects of an invasive predatory zooplankter, Bythotrephes longimanus, on an important prey species, Daphnia mendotae, in Lake Michigan. We fit mechanistic models in an SSM framework to seasonal time series (1994-2012) using a recently developed, maximum-likelihood-based optimization method, iterated filtering, which can overcome challenges in ecological data (e.g., nonlinearities, measurement error, and irregular sampling intervals). Our results indicate that B. longimanus strongly influences D. mendotae dynamics, with mean annual peak densities of B. longimanus observed in Lake Michigan estimated to cause a 61% reduction in D. mendotae population growth rate and a 59% reduction in peak biomass density. Further, the observed B. longimanus effect is most consistent with an NCE via reduced birth rates. The SSM approach also provided estimates for key biological parameters (e.g., demographic rates) and the contribution of dynamic stochasticity and measurement error. Our study therefore provides evidence derived directly from survey data that the invasive zooplankter B. longimanus is affecting zooplankton demographics and offer parameter estimates needed to inform predictive models that explore the effect of B. longimanus under different scenarios, such as climate change.
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Affiliation(s)
- J A Marino
- Department of Biology, Bradley University, 101 Olin Hall, 1501 West Bradley Avenue, Peoria, Illinois, 61625, USA.,Department of Fisheries and Wildlife, Michigan State University, Natural Resources Building, 480 Wilson Road, Room 13, East Lansing, Michigan, 48824, USA.,Department of Statistics, University of Michigan, 311 West Hall, 1085 South University, Ann Arbor, Michigan, 48109, USA
| | - S D Peacor
- Department of Fisheries and Wildlife, Michigan State University, Natural Resources Building, 480 Wilson Road, Room 13, East Lansing, Michigan, 48824, USA
| | - D B Bunnell
- Great Lakes Science Center, United States Geological Survey, 1451 Green Road, Ann Arbor, Michigan, 48105, USA
| | - H A Vanderploeg
- Great Lakes Environmental Research Laboratory, National Oceanic and Atmospheric Administration, 4840 South State Road, Ann Arbor, Michigan, 48108, USA
| | - S A Pothoven
- Lake Michigan Field Station, Great Lakes Environmental Research Laboratory, National Oceanic and Atmospheric Administration, 1431 Beach Street, Muskegon, Michigan, 49441, USA
| | - A K Elgin
- Lake Michigan Field Station, Great Lakes Environmental Research Laboratory, National Oceanic and Atmospheric Administration, 1431 Beach Street, Muskegon, Michigan, 49441, USA
| | - J R Bence
- Department of Statistics, University of Michigan, 311 West Hall, 1085 South University, Ann Arbor, Michigan, 48109, USA
| | - J Jiao
- Department of Statistics, University of Michigan, 311 West Hall, 1085 South University, Ann Arbor, Michigan, 48109, USA
| | - E L Ionides
- Great Lakes Science Center, United States Geological Survey, 1451 Green Road, Ann Arbor, Michigan, 48105, USA
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Bretó C, Ionides EL, King AA. Panel Data Analysis via Mechanistic Models. J Am Stat Assoc 2019; 115:1178-1188. [PMID: 32905476 PMCID: PMC7472993 DOI: 10.1080/01621459.2019.1604367] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Accepted: 03/16/2019] [Indexed: 12/15/2022]
Abstract
Panel data, also known as longitudinal data, consist of a collection of time series. Each time series, which could itself be multivariate, comprises a sequence of measurements taken on a distinct unit. Mechanistic modeling involves writing down scientifically motivated equations describing the collection of dynamic systems giving rise to the observations on each unit. A defining characteristic of panel systems is that the dynamic interaction between units should be negligible. Panel models therefore consist of a collection of independent stochastic processes, generally linked through shared parameters while also having unit-specific parameters. To give the scientist flexibility in model specification, we are motivated to develop a framework for inference on panel data permitting the consideration of arbitrary nonlinear, partially observed panel models. We build on iterated filtering techniques that provide likelihood-based inference on nonlinear partially observed Markov process models for time series data. Our methodology depends on the latent Markov process only through simulation; this plug-and-play property ensures applicability to a large class of models. We demonstrate our methodology on a toy example and two epidemiological case studies. We address inferential and computational issues arising due to the combination of model complexity and dataset size. Supplementary materials for this article are available online.
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Affiliation(s)
- Carles Bretó
- Department of Statistics, University of Michigan, Ann Arbor, MI
- Departament d’Anàlisi Econòmica, Universitat de València, València, Spain
| | | | - Aaron A. King
- Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI
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Affiliation(s)
| | - Fredrik Lindsten
- Division of Statistics and Machine Learning, Linköping University, Linköping, Sweden
| | - Thomas B. Schön
- Department of Information Technology, Uppsala University, Uppsala, Sweden
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Shao S, Jacob PE, Ding J, Tarokh V. Bayesian Model Comparison with the Hyvärinen Score: Computation and Consistency. J Am Stat Assoc 2019. [DOI: 10.1080/01621459.2018.1518237] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Stephane Shao
- Department of Statistics, Harvard University, Cambridge, MA
| | | | - Jie Ding
- School of Statistics, University of Minnesota
| | - Vahid Tarokh
- Department of Electrical and Computer Engineering, Duke University
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Finger F, Funk S, White K, Siddiqui MR, Edmunds WJ, Kucharski AJ. Real-time analysis of the diphtheria outbreak in forcibly displaced Myanmar nationals in Bangladesh. BMC Med 2019; 17:58. [PMID: 30857521 PMCID: PMC6413455 DOI: 10.1186/s12916-019-1288-7] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/09/2018] [Accepted: 02/12/2019] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Between August and December 2017, more than 625,000 Rohingya from Myanmar fled into Bangladesh, settling in informal makeshift camps in Cox's Bazar district and joining 212,000 Rohingya already present. In early November, a diphtheria outbreak hit the camps, with 440 reported cases during the first month. A rise in cases during early December led to a collaboration between teams from Médecins sans Frontières-who were running a provisional diphtheria treatment centre-and the London School of Hygiene and Tropical Medicine with the goal to use transmission dynamic models to forecast the potential scale of the outbreak and the resulting resource needs. METHODS We first adjusted for delays between symptom onset and case presentation using the observed distribution of reporting delays from previously reported cases. We then fit a compartmental transmission model to the adjusted incidence stratified by age group and location. Model forecasts with a lead time of 2 weeks were issued on 12, 20, 26 and 30 December and communicated to decision-makers. RESULTS The first forecast estimated that the outbreak would peak on 19 December in Balukhali camp with 303 (95% posterior predictive interval 122-599) cases and would continue to grow in Kutupalong camp, requiring a bed capacity of 316 (95% posterior predictive interval (PPI) 197-499). On 19 December, a total of 54 cases were reported, lower than forecasted. Subsequent forecasts were more accurate: on 20 December, we predicted a total of 912 cases (95% PPI 367-2183) and 136 (95% PPI 55-327) hospitalizations until the end of the year, with 616 cases actually reported during this period. CONCLUSIONS Real-time modelling enabled feedback of key information about the potential scale of the epidemic, resource needs and mechanisms of transmission to decision-makers at a time when this information was largely unknown. By 20 December, the model generated reliable forecasts and helped support decision-making on operational aspects of the outbreak response, such as hospital bed and staff needs, and with advocacy for control measures. Although modelling is only one component of the evidence base for decision-making in outbreak situations, suitable analysis and forecasting techniques can be used to gain insights into an ongoing outbreak.
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Affiliation(s)
- Flavio Finger
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
| | - Sebastian Funk
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
| | - Kate White
- Médecins Sans Frontières, Amsterdam, Netherlands
| | | | - W. John Edmunds
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
| | - Adam J. Kucharski
- Centre for the Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
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Abstract
Second-order statistics such as the variance and autocorrelation can be useful indicators of the stability of randomly perturbed systems, in some cases providing early warning of an impending, dramatic change in the system’s dynamics. One specific application area of interest is the surveillance of infectious diseases. In the context of disease (re-)emergence, a goal could be to have an indicator that is informative of whether the system is approaching the epidemic threshold, a point beyond which a major outbreak becomes possible. Prior work in this area has provided some proof of this principle but has not analytically treated the effect of imperfect observation on the behavior of indicators. This work provides expected values for several moments of the number of reported cases, where reported cases follow a binomial or negative binomial distribution with a mean based on the number of deaths in a birth-death-immigration process over some reporting interval. The normalized second factorial moment and the decay time of the number of reported cases are two indicators that are insensitive to the reporting probability. Simulation is used to show how this insensitivity could be used to distinguish a trend of increased reporting from a trend of increased transmission. The simulation study also illustrates both the high variance of estimates and the possibility of reducing the variance by averaging over an ensemble of estimates from multiple time series.
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Affiliation(s)
- Eamon B. O’Dea
- Odum School of Ecology and Center for the Ecology of Infectious Diseases, University of Georgia, 140 E. Green Street, Athens, GA, 30602, USA
| | - John M. Drake
- Odum School of Ecology and Center for the Ecology of Infectious Diseases, University of Georgia, 140 E. Green Street, Athens, GA, 30602, USA
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Champagne C, Paul R, Ly S, Duong V, Leang R, Cazelles B. Dengue modeling in rural Cambodia: Statistical performance versus epidemiological relevance. Epidemics 2019; 26:43-57. [DOI: 10.1016/j.epidem.2018.08.004] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2017] [Revised: 07/19/2018] [Accepted: 08/27/2018] [Indexed: 02/07/2023] Open
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Champagne C, Cazelles B. Comparison of stochastic and deterministic frameworks in dengue modelling. Math Biosci 2019; 310:1-12. [PMID: 30735695 DOI: 10.1016/j.mbs.2019.01.010] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2018] [Revised: 01/28/2019] [Accepted: 01/30/2019] [Indexed: 11/16/2022]
Abstract
We perform estimations of compartment models for dengue transmission in rural Cambodia with increasing complexity regarding both model structure and the account for stochasticity. On the one hand, we successively account for three embedded sources of stochasticity: observation noise, demographic variability and environmental hazard. On the other hand, complexity in the model structure is increased by introducing vector-borne transmission, explicit asymptomatic infections and interacting virus serotypes. Using two sources of case data from dengue epidemics in Kampong Cham (Cambodia), models are estimated in the bayesian framework, with Markov Chain Monte Carlo and Particle Markov Chain Monte Carlo. We highlight the advantages and drawbacks of the different formulations in a practical setting. Although in this case the deterministic models provide a good approximation of the mean trajectory for a low computational cost, the stochastic frameworks better reflect and account for parameter and simulation uncertainty.
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Affiliation(s)
- Clara Champagne
- Institut de Biologie de l'Ecole Normale Supérieure (IBENS), Ecole Normale Supérieure, CNRS UMR 8197,46 rue d'Ulm, Paris 75005, France; CREST, ENSAE, Université Paris Saclay, 5, avenue Henry Le Chatelier, Palaiseau cedex 91764, France.
| | - Bernard Cazelles
- Institut de Biologie de l'Ecole Normale Supérieure (IBENS), Ecole Normale Supérieure, CNRS UMR 8197,46 rue d'Ulm, Paris 75005, France; International Center for Mathematical and Computational Modeling of Complex Systems (UMMISCO), UMI 209 Sorbonne Université - IRD, Bondy cedex, France
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Lemaitre J, Pasetto D, Perez-Saez J, Sciarra C, Wamala JF, Rinaldo A. Rainfall as a driver of epidemic cholera: Comparative model assessments of the effect of intra-seasonal precipitation events. Acta Trop 2019; 190:235-243. [PMID: 30465744 DOI: 10.1016/j.actatropica.2018.11.013] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2018] [Revised: 11/04/2018] [Accepted: 11/14/2018] [Indexed: 01/18/2023]
Abstract
The correlation between cholera epidemics and climatic drivers, in particular seasonal tropical rainfall, has been studied in a variety of contexts owing to its documented relevance. Several mechanistic models of cholera transmission have included rainfall as a driver by focusing on two possible transmission pathways: either by increasing exposure to contaminated water (e.g. due to worsening sanitary conditions during water excess), or water contamination by freshly excreted bacteria (e.g. due to washout of open-air defecation sites or overflows). Our study assesses the explanatory power of these different modeling structures by formal model comparison using deterministic and stochastic models of the type susceptible-infected-recovered-bacteria (SIRB). The incorporation of rainfall effects is generalized using a nonlinear function that can increase or decrease the relative importance of the large precipitation events. Our modelling framework is tested against the daily epidemiological data collected during the 2015 cholera outbreak within the urban context of Juba, South Sudan. This epidemic is characterized by a particular intra-seasonal double peak on the incidence in apparent relation with particularly strong rainfall events. Our results show that rainfall-based models in both their deterministic and stochastic formulations outperform models that do not account for rainfall. In fact, classical SIRB models are not able to reproduce the second epidemiological peak, thus suggesting that it was rainfall-driven. Moreover we found stronger support across model types for rainfall acting on increased exposure rather than on exacerbated water contamination. Although these results are context-specific, they stress the importance of a systematic and comprehensive appraisal of transmission pathways and their environmental forcings when embarking in the modelling of epidemic cholera.
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Affiliation(s)
- Joseph Lemaitre
- Laboratory of Ecohydrology, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland.
| | - Damiano Pasetto
- Laboratory of Ecohydrology, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland.
| | - Javier Perez-Saez
- Laboratory of Ecohydrology, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland.
| | - Carla Sciarra
- Dipartimento di Ingegneria dell'Ambiente, del Territorio e delle Infrastrutture, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy.
| | | | - Andrea Rinaldo
- Laboratory of Ecohydrology, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland; Dipartimento ICEA, Università di Padova, 35100 Padova, Italy.
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Pei S, Cane MA, Shaman J. Predictability in process-based ensemble forecast of influenza. PLoS Comput Biol 2019; 15:e1006783. [PMID: 30817754 PMCID: PMC6394909 DOI: 10.1371/journal.pcbi.1006783] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2018] [Accepted: 01/12/2019] [Indexed: 11/18/2022] Open
Abstract
Process-based models have been used to simulate and forecast a number of nonlinear dynamical systems, including influenza and other infectious diseases. In this work, we evaluate the effects of model initial condition error and stochastic fluctuation on forecast accuracy in a compartmental model of influenza transmission. These two types of errors are found to have qualitatively similar growth patterns during model integration, indicating that dynamic error growth, regardless of source, is a dominant component of forecast inaccuracy. We therefore examine the nonlinear growth of model initial error and compute the fastest growing directions using singular vector analysis. Using this information, we generate perturbations in an ensemble forecast system of influenza to obtain more optimal ensemble spread. In retrospective forecasts of historical outbreaks for 95 US cities from 2003 to 2014, this approach improves short-term forecast of incidence over the next one to four weeks.
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Affiliation(s)
- Sen Pei
- Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, NY, United States of America
| | - Mark A. Cane
- Lamont-Doherty Earth Observatory, Columbia University, New York, NY, United States of America
| | - Jeffrey Shaman
- Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, NY, United States of America
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RETRACTED ARTICLE: Smoothing with Couplings of Conditional Particle Filters. J Am Stat Assoc 2018. [DOI: 10.1080/01621459.2018.1505625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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49
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Lambert S, Ezanno P, Garel M, Gilot-Fromont E. Demographic stochasticity drives epidemiological patterns in wildlife with implications for diseases and population management. Sci Rep 2018; 8:16846. [PMID: 30442961 PMCID: PMC6237989 DOI: 10.1038/s41598-018-34623-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2017] [Accepted: 10/19/2018] [Indexed: 11/28/2022] Open
Abstract
Infectious diseases raise many concerns for wildlife and new insights must be gained to manage infected populations. Wild ungulates provide opportunities to gain such insights as they host many pathogens. Using modelling and data collected from an intensively monitored population of Pyrenean chamois, we investigated the role of stochastic processes in governing epidemiological patterns of pestivirus spread in both protected and hunted populations. We showed that demographic stochasticity led to three epidemiological outcomes: early infection fade-out, epidemic outbreaks with population collapse, either followed by virus extinction or by endemic situations. Without re-introduction, the virus faded out in >50% of replications within 4 years and did not persist >20 years. Test-and-cull of infected animals and vaccination had limited effects relative to the efforts devoted, especially in hunted populations in which only quota reduction somewhat improve population recovery. Success of these strategies also relied on the maintenance of a high level of surveillance of hunter-harvested animals. Our findings suggested that, while surveillance and maintenance of population levels at intermediate densities to avoid large epidemics are useful at any time, a 'do nothing' approach during epidemics could be the 'least bad' management strategy in populations of ungulates species facing pestivirus infection.
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Affiliation(s)
- Sébastien Lambert
- Université de Lyon, Université Lyon 1, UMR CNRS 5558 Laboratoire de Biométrie et Biologie Evolutive, Villeurbanne, France.
- Office National de la Chasse et de la Faune Sauvage, Unité Ongulés Sauvages, 5 allée de Bethléem - ZI Mayencin, 38610, Gières, France.
| | | | - Mathieu Garel
- Office National de la Chasse et de la Faune Sauvage, Unité Ongulés Sauvages, 5 allée de Bethléem - ZI Mayencin, 38610, Gières, France
| | - Emmanuelle Gilot-Fromont
- Université de Lyon, Université Lyon 1, UMR CNRS 5558 Laboratoire de Biométrie et Biologie Evolutive, Villeurbanne, France
- Université de Lyon, VetAgro Sup, Marcy l'Etoile, France
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50
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Ganyani T, Faes C, Chowell G, Hens N. Assessing inference of the basic reproduction number in an SIR model incorporating a growth-scaling parameter. Stat Med 2018; 37:4490-4506. [PMID: 30117184 DOI: 10.1002/sim.7935] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2017] [Revised: 06/08/2018] [Accepted: 07/16/2018] [Indexed: 11/12/2022]
Abstract
The standard mass action, which assumes that infectious disease transmission occurs in well-mixed populations, is popular for formulating compartmental epidemic models. Compartmental epidemic models often follow standard mass action for simplicity and to gain insight into transmission dynamics as it often performs well at reproducing disease dynamics in large populations. In this work, we formulate discrete time stochastic susceptible-infected-removed models with linear (standard) and nonlinear mass action structures to mimic varying mixing levels. Using simulations and real epidemic data, we demonstrate the sensitivity of the basic reproduction number to these mathematical structures of the force of infection. Our results suggest the need to consider nonlinear mass action in order to generate more accurate estimates of the basic reproduction number although its uncertainty increases due to the addition of one growth scaling parameter.
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Affiliation(s)
- Tapiwa Ganyani
- Interuniversity Institute for Biostatistics and Statistical Bioinformatics, UHasselt (Hasselt University), Diepenbeek, Belgium
| | - Christel Faes
- Interuniversity Institute for Biostatistics and Statistical Bioinformatics, UHasselt (Hasselt University), Diepenbeek, Belgium
| | - Gerardo Chowell
- School of Public Health, Georgia State University, Atlanta, Georgia.,Division of International Epidemiology and Population Studies, Fogarty International Center, National Institute of Health, Bethesda, Maryland
| | - Niel Hens
- Interuniversity Institute for Biostatistics and Statistical Bioinformatics, UHasselt (Hasselt University), Diepenbeek, Belgium.,Centre for Health Economics Research and Modelling Infectious Diseases, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium
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