Plug-and-play inference for disease dynamics: measles in large and small populations as a case study

Quantifying suicide contagion at population scale

The spread of suicidal behavior among individuals is often described as a contagion; however, rigorous modeling of suicide as a dynamic, contagious process is minimal. Here, we develop and validate a model-inference system depicting suicide ideation and death and use it to quantify the contagion processes in the US associated with two prominent celebrity suicide events: Robin Williams during 2014 and Kate Spade and Anthony Bourdain, which occurred 3 days apart during 2018. We show that both events produced large transient increases of suicide contagion contact rates, i.e., the spread of suicidal thought and behavior, and a period of elevated suicidal ideation in the general population. Our modeling approach provides a framework for quantifying suicidal contagion and better understanding, preventing, and containing its spread.

Inference on spatiotemporal dynamics for coupled biological populations

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.

EXACT PHYLODYNAMIC LIKELIHOOD VIA STRUCTURED MARKOV GENEALOGY PROCESSES

We consider genealogies arising from a Markov population process in which individuals are categorized into a discrete collection of compartments, with the requirement that individuals within the same compartment are statistically exchangeable. When equipped with a sampling process, each such population process induces a time-evolving tree-valued process defined as the genealogy of all sampled individuals. We provide a construction of this genealogy process and derive exact expressions for the likelihood of an observed genealogy in terms of filter equations. These filter equations can be numerically solved using standard Monte Carlo integration methods. Thus, we obtain statistically efficient likelihood-based inference for essentially arbitrary compartment models based on an observed genealogy of individuals sampled from the population.

Informing policy via dynamic models: Cholera in Haiti

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.

Modelling count data with partial differential equation models in biology

Partial differential equation (PDE) models are often used to study biological phenomena involving movement-birth-death processes, including ecological population dynamics and the invasion of populations of biological cells. Count data, by definition, is non-negative, and count data relating to biological populations is often bounded above by some carrying capacity that arises through biological competition for space or nutrients. Parameter estimation, parameter identifiability, and making model predictions usually involves working with a measurement error model that explicitly relating experimental measurements with the solution of a mathematical model. In many biological applications, a typical approach is to assume the data are normally distributed about the solution of the mathematical model. Despite the widespread use of the standard additive Gaussian measurement error model, the assumptions inherent in this approach are rarely explicitly considered or compared with other options. Here, we interpret scratch assay data, involving migration, proliferation and delays in a population of cancer cells using a reaction-diffusion PDE model. We consider relating experimental measurements to the PDE solution using a standard additive Gaussian measurement error model alongside a comparison to a more biologically realistic binomial measurement error model. While estimates of model parameters are relatively insensitive to the choice of measurement error model, model predictions for data realisations are very sensitive. The standard additive Gaussian measurement error model leads to biologically inconsistent predictions, such as negative counts and counts that exceed the carrying capacity across a relatively large spatial region within the experiment. Furthermore, the standard additive Gaussian measurement error model requires estimating an additional parameter compared to the binomial measurement error model. In contrast, the binomial measurement error model leads to biologically plausible predictions and is simpler to implement. We provide open source Julia software on GitHub to replicate all calculations in this work, and we explain how to generalise our approach to deal with coupled PDE models with several dependent variables through a multinomial measurement error model, as well as pointing out other potential generalisations by linking our work with established practices in the field of generalised linear models.

Maternal pertussis immunization and the blunting of routine vaccine effectiveness: a meta-analysis and modeling study

A key goal of pertussis control is to protect infants too young to be vaccinated, the age group most vulnerable to this highly contagious respiratory infection. In the last decade, maternal immunization has been deployed in many countries, successfully reducing pertussis in this age group. Because of immunological blunting, however, this strategy may erode the effectiveness of primary vaccination at later ages. Here, we systematically reviewed the literature on the relative risk (RR) of pertussis after primary immunization of infants born to vaccinated vs. unvaccinated mothers. The four studies identified had ≤6 years of follow-up and large statistical uncertainty (meta-analysis weighted mean RR: 0.71, 95% CI: 0.38-1.32). To interpret this evidence, we designed a new mathematical model with explicit blunting mechanisms and evaluated maternal immunization's short- and long-term impact on pertussis transmission dynamics. We show that transient dynamics can mask blunting for at least a decade after rolling out maternal immunization. Hence, the current epidemiological evidence may be insufficient to rule out modest reductions in the effectiveness of primary vaccination. Irrespective of this potential collateral cost, we predict that maternal immunization will remain effective at protecting unvaccinated newborns, supporting current public health recommendations.

Implementing measurement error models with mechanistic mathematical models in a likelihood-based framework for estimation, identifiability analysis and prediction in the life sciences

Throughout the life sciences, we routinely seek to interpret measurements and observations using parametrized mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a mathematical model with noisy and incomplete measurement data. This is often achieved by assuming that the data are noisy measurements of the solution of a deterministic mathematical model, and that measurement errors are additive and normally distributed. While this assumption of additive Gaussian noise is extremely common and simple to implement and interpret, it is often unjustified and can lead to poor parameter estimates and non-physical predictions. One way to overcome this challenge is to implement a different measurement error model. In this review, we demonstrate how to implement a range of measurement error models in a likelihood-based framework for estimation, identifiability analysis and prediction, called profile-wise analysis. This frequentist approach to uncertainty quantification for mechanistic models leverages the profile likelihood for targeting parameters and understanding their influence on predictions. Case studies, motivated by simple caricature models routinely used in systems biology and mathematical biology literature, illustrate how the same ideas apply to different types of mathematical models. Open-source Julia code to reproduce results is available on GitHub.

A data-driven semi-parametric model of SARS-CoV-2 transmission in the United States

To support decision-making and policy for managing epidemics of emerging pathogens, we present a model for inference and scenario analysis of SARS-CoV-2 transmission in the USA. The stochastic SEIR-type model includes compartments for latent, asymptomatic, detected and undetected symptomatic individuals, and hospitalized cases, and features realistic interval distributions for presymptomatic and symptomatic periods, time varying rates of case detection, diagnosis, and mortality. The model accounts for the effects on transmission of human mobility using anonymized mobility data collected from cellular devices, and of difficult to quantify environmental and behavioral factors using a latent process. The baseline transmission rate is the product of a human mobility metric obtained from data and this fitted latent process. We fit the model to incident case and death reports for each state in the USA and Washington D.C., using likelihood Maximization by Iterated particle Filtering (MIF). Observations (daily case and death reports) are modeled as arising from a negative binomial reporting process. We estimate time-varying transmission rate, parameters of a sigmoidal time-varying fraction of hospitalized cases that result in death, extra-demographic process noise, two dispersion parameters of the observation process, and the initial sizes of the latent, asymptomatic, and symptomatic classes. In a retrospective analysis covering March-December 2020, we show how mobility and transmission strength became decoupled across two distinct phases of the pandemic. The decoupling demonstrates the need for flexible, semi-parametric approaches for modeling infectious disease dynamics in real-time.

The reinfection threshold, revisited

One mode by which infection-derived immunity fails is when recovery leads to a reduced but nonzero risk of reinfection. This type of partial protection is called leaky immunity with the degree of leakiness quantified by the relative probability a previously infected individual will get infected upon exposure compared to a naively susceptible individual. Previous authors have defined the reinfection threshold, which occurs when the basic reproduction number equals the inverse of the leakiness, however, there has been some debate about whether or not this is a real threshold. Here we show how the reinfection threshold relates to two important occurrences: (1) the point at which the endemic equilibrium changes from being a stable spiral to a stable node, and (2) the point at which the rate of change of the prevalence increases the most relative to leakiness. When the recovery period is short relative to the average lifetime then both occurrences are close to the reinfection threshold. We show how these results are related to the reinfection threshold found in other models of imperfect immunity. To further demonstrate the significance of this threshold in modeling, we conducted a simulation study to evaluate some of the consequences the reinfection threshold might have in parameter estimation and modeling. Using specific parameter values chosen to reflect an acute infection, we found that the basic reproduction number values larger than that of the reinfection threshold value were less identifiable than those below the threshold.

Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models

Interpreting data using mechanistic mathematical models provides a foundation for discovery and decision-making in all areas of science and engineering. Developing mechanistic insight by combining mathematical models and experimental data is especially critical in mathematical biology as new data and new types of data are collected and reported. Key steps in using mechanistic mathematical models to interpret data include: (i) identifiability analysis; (ii) parameter estimation; and (iii) model prediction. Here we present a systematic, computationally-efficient workflow we call Profile-Wise Analysis (PWA) that addresses all three steps in a unified way. Recently-developed methods for constructing 'profile-wise' prediction intervals enable this workflow and provide the central linkage between different workflow components. These methods propagate profile-likelihood-based confidence sets for model parameters to predictions in a way that isolates how different parameter combinations affect model predictions. We show how to extend these profile-wise prediction intervals to two-dimensional interest parameters. We then demonstrate how to combine profile-wise prediction confidence sets to give an overall prediction confidence set that approximates the full likelihood-based prediction confidence set well. Our three case studies illustrate practical aspects of the workflow, focusing on ordinary differential equation (ODE) mechanistic models with both Gaussian and non-Gaussian noise models. While the case studies focus on ODE-based models, the workflow applies to other classes of mathematical models, including partial differential equations and simulation-based stochastic models. Open-source software on GitHub can be used to replicate the case studies.

Anchoring the mean generation time in the SEIR to mitigate biases in ℜ0 estimates due to uncertainty in the distribution of the epidemiological delays

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 .

Relative role of community transmission and campus contagion in driving the spread of SARS-CoV-2: Lessons from Princeton University

Mathematical models have played a crucial role in exploring and guiding pandemic responses. University campuses present a particularly well-documented case for institutional outbreaks, thereby providing a unique opportunity to understand detailed patterns of pathogen spread. Here, we present descriptive and modeling analyses of SARS-CoV-2 transmission on the Princeton University (PU) campus-this model was used throughout the pandemic to inform policy decisions and operational guidelines for the university campus. Epidemic patterns between the university campus and surrounding communities exhibit strong spatiotemporal correlations. Mathematical modeling analysis further suggests that the amount of on-campus transmission was likely limited during much of the wider pandemic until the end of 2021. Finally, we find that a superspreading event likely played a major role in driving the Omicron variant outbreak on the PU campus during the spring semester of the 2021-2022 academic year. Despite large numbers of cases on campus in this period, case levels in surrounding communities remained low, suggesting that there was little spillover transmission from campus to the local community.

Charting the spatial dynamics of early SARS-CoV-2 transmission in Washington state

The spread of SARS-CoV-2 has been geographically uneven. To understand the drivers of this spatial variation in SARS-CoV-2 transmission, in particular the role of stochasticity, we used the early stages of the SARS-CoV-2 invasion in Washington state as a case study. We analysed spatially-resolved COVID-19 epidemiological data using two distinct statistical analyses. The first analysis involved using hierarchical clustering on the matrix of correlations between county-level case report time series to identify geographical patterns in the spread of SARS-CoV-2 across the state. In the second analysis, we used a stochastic transmission model to perform likelihood-based inference on hospitalised cases from five counties in the Puget Sound region. Our clustering analysis identifies five distinct clusters and clear spatial patterning. Four of the clusters correspond to different geographical regions, with the final cluster spanning the state. Our inferential analysis suggests that a high degree of connectivity across the region is necessary for the model to explain the rapid inter-county spread observed early in the pandemic. In addition, our approach allows us to quantify the impact of stochastic events in determining the subsequent epidemic. We find that atypically rapid transmission during January and February 2020 is necessary to explain the observed epidemic trajectories in King and Snohomish counties, demonstrating a persisting impact of stochastic events. Our results highlight the limited utility of epidemiological measures calculated over broad spatial scales. Furthermore, our results make clear the challenges with predicting epidemic spread within spatially extensive metropolitan areas, and indicate the need for high-resolution mobility and epidemiological data.

Resolving the enigma of Iquitos and Manaus: A modeling analysis of multiple COVID-19 epidemic waves in two Amazonian cities

The two nearby Amazonian cities of Iquitos and Manaus endured explosive COVID-19 epidemics and may well have suffered the world's highest infection and death rates over 2020, the first year of the pandemic. State-of-the-art epidemiological and modeling studies estimated that the populations of both cities came close to attaining herd immunity (>70% infected) at the termination of the first wave and were thus protected. This makes it difficult to explain the more deadly second wave of COVID-19 that struck again in Manaus just months later, simultaneous with the appearance of a new P.1 variant of concern, creating a catastrophe for the unprepared population. It was suggested that the second wave was driven by reinfections, but the episode has become controversial and an enigma in the history of the pandemic. We present a data-driven model of epidemic dynamics in Iquitos, which we also use to explain and model events in Manaus. By reverse engineering the multiple epidemic waves over 2 y in these two cities, the partially observed Markov process model inferred that the first wave left Manaus with a highly susceptible and vulnerable population (≈40% infected) open to invasion by P.1, in contrast to Iquitos (≈72% infected). The model reconstructed the full epidemic outbreak dynamics from mortality data by fitting a flexible time-varying reproductive number [Formula: see text] while estimating reinfection and impulsive immune evasion. The approach is currently highly relevant given the lack of tools available to assess these factors as new SARS-CoV-2 virus variants appear with different degrees of immune evasion.

Likelihood-based estimation and prediction for a measles outbreak in Samoa

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.

Disentangling the causes of mumps reemergence in the United States

Over the past two decades, multiple countries with high vaccine coverage have experienced resurgent outbreaks of mumps. Worryingly, in these countries, a high proportion of cases have been among those who have completed the recommended vaccination schedule, raising alarm about the effectiveness of existing vaccines. Two putative mechanisms of vaccine failure have been proposed as driving observed trends: 1) gradual waning of vaccine-derived immunity (necessitating additional booster doses) and 2) the introduction of novel viral genotypes capable of evading vaccinal immunity. Focusing on the United States, we conduct statistical likelihood-based hypothesis testing using a mechanistic transmission model on age-structured epidemiological, demographic, and vaccine uptake time series data. We find that the data are most consistent with the waning hypothesis and estimate that 32.8% (32%, 33.5%) of individuals lose vaccine-derived immunity by age 18 y. Furthermore, we show using our transmission model how waning vaccine immunity reproduces qualitative and quantitatively consistent features of epidemiological data, namely 1) the shift in mumps incidence toward older individuals, 2) the recent recurrence of mumps outbreaks, and 3) the high proportion of mumps cases among previously vaccinated individuals.

Twice evasions of Omicron variants explain the temporal patterns in six Asian and Oceanic countries

BACKGROUND

The ongoing coronavirus 2019 (COVID-19) pandemic has emerged and caused multiple pandemic waves in the following six countries: India, Indonesia, Nepal, Malaysia, Bangladesh and Myanmar. Some of the countries have been much less studied in this devastating pandemic. This study aims to assess the impact of the Omicron variant in these six countries and estimate the infection fatality rate (IFR) and the reproduction number [Formula: see text] in these six South Asia, Southeast Asia and Oceania countries.

METHODS

We propose a Susceptible-Vaccinated-Exposed-Infectious-Hospitalized-Death-Recovered model with a time-varying transmission rate [Formula: see text] to fit the multiple waves of the COVID-19 pandemic and to estimate the IFR and [Formula: see text] in the aforementioned six countries. The level of immune evasion and the intrinsic transmissibility advantage of the Omicron variant are also considered in this model.

RESULTS

We fit our model to the reported deaths well. We estimate the IFR (in the range of 0.016 to 0.136%) and the reproduction number [Formula: see text] (in the range of 0 to 9) in the six countries. Multiple pandemic waves in each country were observed in our simulation results.

CONCLUSIONS

The invasion of the Omicron variant caused the new pandemic waves in the six countries. The higher [Formula: see text] suggests the intrinsic transmissibility advantage of the Omicron variant. Our model simulation forecast implies that the Omicron pandemic wave may be mitigated due to the increasing immunized population and vaccine coverage.

Mechanisms for the circulation of influenza A(H3N2) in China: A spatiotemporal modelling study

Circulation of seasonal influenza is the product of complex interplay among multiple drivers, yet characterizing the underlying mechanism remains challenging. Leveraging the diverse seasonality of A(H3N2) virus and abundant climatic space across regions in China, we quantitatively investigated the relative importance of population susceptibility, climatic factors, and antigenic change on the dynamics of influenza A(H3N2) through an integrative modelling framework. Specifically, an absolute humidity driven multiscale transmission model was constructed for the 2013/2014, 2014/2015 and 2016/2017 influenza seasons that were dominated by influenza A(H3N2). We revealed the variable impact of absolute humidity on influenza transmission and differences in the occurring timing and magnitude of antigenic change for those three seasons. Overall, the initial population susceptibility, climatic factors, and antigenic change explained nearly 55% of variations in the dynamics of influenza A(H3N2). Specifically, the additional variation explained by the initial population susceptibility, climatic factors, and antigenic change were at 33%, 26%, and 48%, respectively. The vaccination program alone failed to fully eliminate the summer epidemics of influenza A(H3N2) and non-pharmacological interventions were needed to suppress the summer circulation. The quantitative understanding of the interplay among driving factors on the circulation of influenza A(H3N2) highlights the importance of simultaneous monitoring of fluctuations for related factors, which is crucial for precise and targeted prevention and control of seasonal influenza.

Computationally efficient framework for diagnosing, understanding and predicting biphasic population growth

Throughout the life sciences, biological populations undergo multiple phases of growth, often referred to as biphasic growth for the commonly encountered situation involving two phases. Biphasic population growth occurs over a massive range of spatial and temporal scales, ranging from microscopic growth of tumours over several days, to decades-long regrowth of corals in coral reefs that can extend for hundreds of kilometres. Different mathematical models and statistical methods are used to diagnose, understand and predict biphasic growth. Common approaches can lead to inaccurate predictions of future growth that may result in inappropriate management and intervention strategies being implemented. Here, we develop a very general computationally efficient framework, based on profile likelihood analysis, for diagnosing, understanding and predicting biphasic population growth. The two key components of the framework are as follows: (i) an efficient method to form approximate confidence intervals for the change point of the growth dynamics and model parameters and (ii) parameter-wise profile predictions that systematically reveal the influence of individual model parameters on predictions. To illustrate our framework we explore real-world case studies across the life sciences.

The stochastic θ -SEIHRD model: Adding randomness to the COVID-19 spread

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.

A simple model to estimate the transmissibility of the Beta, Delta, and Omicron variants of SARS-COV-2 in South Africa

The COVID-19 pandemic caused multiple waves of mortality in South Africa, where three genetic variants of SARS-COV-2 and their ancestral strain dominated consecutively. State-of-the-art mathematical modeling approach was used to estimate the time-varying transmissibility of SARS-COV-2 and the relative transmissibility of Beta, Delta, and Omicron variants. The transmissibility of the three variants were about 73%, 87%, and 276% higher than their preceding variants. To the best of our knowledge, our model is the first simple model that can simulate multiple mortality waves and three variants' replacements in South Africa. The transmissibility of the Omicron variant is substantially higher than that of previous variants.

Reduction in the infection fatality rate of Omicron variant compared with previous variants in South Africa

OBJECTIVE

The SARS-CoV-2 Omicron (B.1.1.529) variant has caused global concern. Previous studies have shown that the variant has enhanced immune evasion ability and transmissibility and reduced severity.

METHODS

In this study, we developed a mathematical model with time-varying transmission rate, vaccination, and immune evasion. We fit the model to reported case and death data up to February 6, 2022 to estimate the transmissibility and infection fatality ratio of the Omicron variant in South Africa.

RESULTS

We found that the high relative transmissibility of the Omicron variant was mainly due to its immune evasion ability, whereas its infection fatality rate substantially decreased by approximately 78.7% (95% confidence interval: 66.9%, 85.0%) with respect to previous variants.

CONCLUSION

On the basis of data from South Africa and mathematical modeling, we found that the Omicron variant is highly transmissible but with significantly lower infection fatality rates than those of previous variants of SARS-CoV-2.

Inferring spatial source of disease outbreaks using maximum entropy

Mathematical modeling of disease outbreaks can infer the future trajectory of an epidemic, allowing for making more informed policy decisions. Another task is inferring the origin of a disease, which is relatively difficult with current mathematical models. Such frameworks, across varying levels of complexity, are typically sensitive to input data on epidemic parameters, case counts, and mortality rates, which are generally noisy and incomplete. To alleviate these limitations, we propose a maximum entropy framework that fits epidemiological models, provides calibrated infection origin probabilities, and is robust to noise due to a prior belief model. Maximum entropy is agnostic to the parameters or model structure used and allows for flexible use when faced with sparse data conditions and incomplete knowledge in the dynamical phase of disease-spread, providing for more reliable modeling at early stages of outbreaks. We evaluate the performance of our model by predicting future disease trajectories based on simulated epidemiological data in synthetic graph networks and the real mobility network of New York State. In addition, unlike existing approaches, we demonstrate that the method can be used to infer the origin of the outbreak with accurate confidence. Indeed, despite the prevalent belief on the feasibility of contact-tracing being limited to the initial stages of an outbreak, we report the possibility of reconstructing early disease dynamics, including the epidemic seed, at advanced stages.

Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data

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.

Estimating the basic reproduction number at the beginning of an outbreak

We compare several popular methods of estimating the basic reproduction number, R₀, focusing on the early stages of an epidemic, and assuming weekly reports of new infecteds. We study the situation when data is generated by one of three standard epidemiological compartmental models: SIR, SEIR, and SEAIR; and examine the sensitivity of the estimators to the model structure. As some methods are developed assuming specific epidemiological models, our work adds a study of their performance in both a well-specified (data generating model and method model are the same) and miss-specified (data generating model and method model differ) settings. We also study R₀ estimation using Canadian COVID-19 case report data. In this study we focus on examples of influenza and COVID-19, though the general approach is easily extendable to other scenarios. Our simulation study reveals that some estimation methods tend to work better than others, however, no singular best method was clearly detected. In the discussion, we provide recommendations for practitioners based on our results.

Infection fatality rate and infection attack rate of COVID-19 in South American countries

BACKGROUND

The ongoing COVID-19 pandemic hit South America badly with multiple waves. Different COVID-19 variants have been storming across the region, leading to more severe infections and deaths even in places with high vaccination coverage. This study aims to assess the spatiotemporal variability of the COVID-19 pandemic and estimate the infection fatality rate (IFR), infection attack rate (IAR) and reproduction number ([Formula: see text]) for twelve most affected South American countries.

METHODS

We fit a susceptible-exposed-infectious-recovered (SEIR)-based model with a time-varying transmission rate to the reported COVID-19 deaths for the twelve South American countries with the highest mortalities. Most of the epidemiological datasets analysed in this work are retrieved from the disease surveillance systems by the World Health Organization, Johns Hopkins Coronavirus Resource Center and Our World in Data. We investigate the COVID-19 mortalities in these countries, which could represent the situation  for the overall South American region. We employ COVID-19 dynamic model with-and-without vaccination considering time-varying flexible transmission rate to estimate IFR, IAR and [Formula: see text] of COVID-19 for the South American countries.

RESULTS

We simulate the model in each scenario under suitable parameter settings and yield biologically reasonable estimates for IFR (varies between 0.303% and 0.723%), IAR (varies between 0.03 and 0.784) and [Formula: see text] (varies between 0.7 and 2.5) for the 12 South American countries. We observe that the severity, dynamical patterns of deaths and time-varying transmission rates among the countries are highly heterogeneous. Further analysis of the model with the effect of vaccination highlights that increasing the vaccination rate could help suppress the pandemic in South America.

CONCLUSIONS

This study reveals possible reasons for the two waves of COVID-19 outbreaks in South America. We observed reductions in the transmission rate corresponding to each wave plausibly due to improvement in nonpharmaceutical interventions measures and human protective behavioral reaction to recent deaths. Thus, strategies coupling social distancing and vaccination could substantially suppress the mortality rate of COVID-19 in South America.

Infection fatality rate and infection attack rate of COVID-19 in South American countries

BACKGROUND

The ongoing COVID-19 pandemic hit South America badly with multiple waves. Different COVID-19 variants have been storming across the region, leading to more severe infections and deaths even in places with high vaccination coverage. This study aims to assess the spatiotemporal variability of the COVID-19 pandemic and estimate the infection fatality rate (IFR), infection attack rate (IAR) and reproduction number ([Formula: see text]) for twelve most affected South American countries.

METHODS

We fit a susceptible-exposed-infectious-recovered (SEIR)-based model with a time-varying transmission rate to the reported COVID-19 deaths for the twelve South American countries with the highest mortalities. Most of the epidemiological datasets analysed in this work are retrieved from the disease surveillance systems by the World Health Organization, Johns Hopkins Coronavirus Resource Center and Our World in Data. We investigate the COVID-19 mortalities in these countries, which could represent the situation  for the overall South American region. We employ COVID-19 dynamic model with-and-without vaccination considering time-varying flexible transmission rate to estimate IFR, IAR and [Formula: see text] of COVID-19 for the South American countries.

RESULTS

We simulate the model in each scenario under suitable parameter settings and yield biologically reasonable estimates for IFR (varies between 0.303% and 0.723%), IAR (varies between 0.03 and 0.784) and [Formula: see text] (varies between 0.7 and 2.5) for the 12 South American countries. We observe that the severity, dynamical patterns of deaths and time-varying transmission rates among the countries are highly heterogeneous. Further analysis of the model with the effect of vaccination highlights that increasing the vaccination rate could help suppress the pandemic in South America.

CONCLUSIONS

This study reveals possible reasons for the two waves of COVID-19 outbreaks in South America. We observed reductions in the transmission rate corresponding to each wave plausibly due to improvement in nonpharmaceutical interventions measures and human protective behavioral reaction to recent deaths. Thus, strategies coupling social distancing and vaccination could substantially suppress the mortality rate of COVID-19 in South America.

Deep learning forecasting using time-varying parameters of the SIRD model for Covid-19

Accurate epidemiological models are necessary for governments, organizations, and individuals to respond appropriately to the ongoing novel coronavirus pandemic. One informative metric epidemiological models provide is the basic reproduction number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0), which can describe if the infected population is growing (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0 > 1$$\end{document}R0>1) or shrinking (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0 < 1$$\end{document}R0<1). We introduce a novel algorithm that incorporates the susceptible-infected-recovered-dead model (SIRD model) with the long short-term memory (LSTM) neural network that allows for real-time forecasting and time-dependent parameter estimates, including the contact rate, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β, and deceased rate, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μ. With an accurate prediction of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μ, we can directly derive \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0, and find a numerical solution of compartmental models, such as the SIR-type models. Incorporating the epidemiological model dynamics of the SIRD model into the LSTM network, the new algorithm improves forecasting accuracy. Furthermore, we utilize mobility data from cellphones and positive test rate in our prediction model, and we also present a vaccination model. Leveraging mobility and vaccination schedule is important for capturing behavioral changes by individuals in response to the pandemic as well as policymakers.

Markov genealogy processes

We construct a family of genealogy-valued Markov processes that are induced by a continuous-time Markov population process. We derive exact expressions for the likelihood of a given genealogy conditional on the history of the underlying population process. These lead to a nonlinear filtering equation which can be used to design efficient Monte Carlo inference algorithms. We demonstrate these calculations with several examples. Existing full-information approaches for phylodynamic inference are special cases of the theory.

The neglected role of relative humidity in the interannual variability of urban malaria in Indian cities

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.

Modelling COVID-19 vaccine breakthrough infections in highly vaccinated Israel-The effects of waning immunity and third vaccination dose

In August 2021, a major wave of the SARS-CoV-2 Delta variant erupted in the highly vaccinated population of Israel. The transmission advantage of the Delta variant enabled it to replace the Alpha variant in approximately two months. The outbreak led to an unexpectedly large proportion of breakthrough infections (BTI)-a phenomenon that received worldwide attention. Most of the Israeli population, especially those aged 60+, received their second dose of the vaccination four months before the invasion of the Delta variant. Hence, either the vaccine induced immunity dropped significantly or the Delta variant possesses immunity escaping abilities, or both. In this work, we model data obtained from the Israeli Ministry of Health, to help understand the epidemiological factors involved in the outbreak. We propose a mathematical model that captures a multitude of factors, including age structure, the time varying vaccine efficacy, time varying transmission rate, BTIs, reduced susceptibility and infectivity of vaccinated individuals, protection duration of the vaccine induced immunity, and the vaccine distribution. We fitted our model to COVID-19 cases among the vaccinated and unvaccinated, for <60 and 60+ age groups, and quantified the transmission rate, the vaccine efficacy over time and the impact of the third dose booster vaccine. The peak transmission rate of the Delta variant was found to be 2.14 times higher than that of the Alpha variant. The two-dose vaccine efficacy against infection dropped significantly from >90% to ~40% over 6 months. We further performed model simulations and quantified counterfactual scenarios examining what would happen if the booster had not been rolled out. We estimated that approximately 4.03 million infective cases (95%CI 3.19, 4.86) were prevented by vaccination overall, and 1.22 million infective cases (95%CI 0.89, 1.62) averted by the booster.

The co-circulating transmission dynamics of SARS-CoV-2 Alpha and Eta variants in Nigeria: A retrospective modeling study of COVID-19

BACKGROUND

The COVID-19 pandemic poses serious threats to public health globally, and the emerging mutations in SARS-CoV-2 genomes has become one of the major challenges of disease control. In the second epidemic wave in Nigeria, the roles of co-circulating SARS-CoV-2 Alpha (ie, B.1.1.7) and Eta (ie, B.1.525) variants in contributing to the epidemiological outcomes were of public health concerns for investigation.

METHODS

We developed a mathematical model to capture the transmission dynamics of different types of strains in Nigeria. By fitting to the national-wide COVID-19 surveillance data, the transmission advantages of SARS-CoV-2 variants were estimated by likelihood-based inference framework.

RESULTS

The reproduction numbers were estimated to decrease steadily from 1.5 to 0.8 in the second epidemic wave. In December 2020, when both Alpha and Eta variants were at low prevalent levels, their transmission advantages (against the wild type) were estimated at 1.51 (95% credible intervals (CrI) = 1.48, 1.54), and 1.56 (95% CrI = 1.54, 1.59), respectively. In January 2021, when the original variants almost vanished, we estimated a weak but significant transmission advantage of Eta against Alpha variants with 1.14 (95% CrI = 1.11, 1.16).

CONCLUSIONS

Our findings suggested evidence of the transmission advantages for both Alpha and Eta variants, of which Eta appeared slightly more infectious than Alpha. We highlighted the critical importance of COVID-19 control measures in mitigating the outbreak size and relaxing the burdens to health care systems in Nigeria.

Estimating the impact of influenza on the epidemiological dynamics of SARS-CoV-2

As in past pandemics, co-circulating pathogens may play a role in the epidemiology of coronavirus disease 2019 (COVID-19), caused by the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In particular, experimental evidence indicates that influenza infection can up-regulate the expression of ACE2-the receptor of SARS-CoV-2 in human cells-and facilitate SARS-CoV-2 infection. Here we hypothesized that influenza impacted the epidemiology of SARS-CoV-2 during the early 2020 epidemic of COVID-19 in Europe. To test this hypothesis, we developed a population-based model of SARS-CoV-2 transmission and of COVID-19 mortality, which simultaneously incorporated the impact of non-pharmaceutical control measures and of influenza on the epidemiological dynamics of SARS-CoV-2. Using statistical inference methods based on iterated filtering, we confronted this model with mortality incidence data in four European countries (Belgium, Italy, Norway, and Spain) to systematically test a range of assumptions about the impact of influenza. We found consistent evidence for a 1.8-3.4-fold (uncertainty range across countries: 1.1 to 5.0) average population-level increase in SARS-CoV-2 transmission associated with influenza during the period of co-circulation. These estimates remained robust to a variety of alternative assumptions regarding the epidemiological traits of SARS-CoV-2 and the modeled impact of control measures. Although further confirmatory evidence is required, our results suggest that influenza could facilitate the spread and hamper effective control of SARS-CoV-2. More generally, they highlight the possible role of co-circulating pathogens in the epidemiology of COVID-19.

Forecast of the COVID-19 trend in India: A simple modelling approach

By February 2021, the overall impact of the COVID-19 pandemic in India had been relatively mild in terms of total reported cases and deaths. Surprisingly, the second wave in early April becomes devastating and attracts worldwide attention. Multiple factors (e.g., Delta variants with increased transmissibility) could have driven the rapid growth of the epidemic in India and led to a large number of deaths within a short period. We aim to reconstruct the transmission rate, estimate the infection fatality rate and forecast the epidemic size. We download the reported COVID-19 mortality data in India and formulate a simple mathematical model with a flexible transmission rate. We use iterated filtering to fit our model to deaths data. We forecast the infection attack rate in a month ahead. Our model simulation matched the reported deaths well and is reasonably close to the results of the serological study. We forecast that the infection attack rate (IAR) could have reached 43% by July 24, 2021, under the current trend. Our estimated infection fatality rate is about 0.07%. Under the current trend, the IAR will likely reach a level of 43% by July 24, 2021. Our estimated infection fatality rate appears unusually low, which could be due to a low case to infection ratio reported in previous study. Our approach is readily applicable in other countries and with other types of data (e.g., excess deaths).

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

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.

Bagged filters for partially observed interacting systems

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.

A Zika Endemic Model for the Contribution of Multiple Transmission Routes

Zika virus disease is a viral disease primarily transmitted to humans through the bite of infected female mosquitoes. Recent evidence indicates that the virus can also be sexually transmitted in hosts and vertically transmitted in vectors. In this paper, we propose a Zika model with three transmission routes, that is, vector-borne transmission between humans and mosquitoes, sexual transmission within humans and vertical transmission within mosquitoes. The basic reproduction number [Formula: see text] is computed and shown to be a sharp threshold quantity. Namely, the disease-free equilibrium is globally asymptotically stable as [Formula: see text], whereas there exists a unique endemic equilibrium which is globally asymptotically stable as [Formula: see text]. The relative contributions of each transmission route on the reproduction number, and the short- and long-term host infections are analyzed. Numerical simulations confirm that vectorial transmission contributes the most to the initial and subsequent transmission. The role of sexual transmission in the early phase of a Zika outbreak is greater than the long term, while vertical transmission is the opposite. Reducing mosquito bites is the most effective measure in lowering the risk of Zika virus infection.

Exploring the Interaction between E484K and N501Y Substitutions of SARS-CoV-2 in Shaping the Transmission Advantage of COVID-19 in Brazil: A Modeling Study

The COVID-19 pandemic poses serious threats to global health, and the emerging mutation in SARS-CoV-2 genomes is one of the major challenges of disease control. Considering the growth of epidemic curve and the circulating SARS-CoV-2 variants in Brazil, the role of locally prevalent E484K and N501Y substitutions in contributing to the epidemiological outcomes is of public health interest for investigation. We developed a likelihood-based statistical framework to reconstruct reproduction numbers, estimate transmission advantage associated with different SARS-CoV-2 variants regarding the marking (identifying) 484K and 501Y substitutions (including Alpha, Zeta, and Gamma variants) in Brazil, and explored the interactive effects of genetic activities on transmission advantage marked by these two mutations. We found a significant transmission advantage associated with the 484K/501Y variants (including P.1 or Gamma variants), which increased the infectivity significantly by 23%. In contrast and by comparison to Gamma variants, E484K or N501Y (including Alpha or Zeta variants) substitution alone appeared less likely to secure a concrete transmission advantage in Brazil. Our finding indicates that the combined impact of genetic activities on transmission advantage marked by 484K/501Y outperforms their independent contributions in Brazil, which implies an interactive effect in shaping the increase in the infectivity of COVID-19. Future studies are needed to investigate the mechanisms of how E484K and N501Y mutations and the complex genetic mutation activities marked by them in SARS-CoV-2 affect the transmissibility of COVID-19.

Identifying asymptomatic spreaders of antimicrobial-resistant pathogens in hospital settings

Antimicrobial-resistant organisms (AMROs) can colonize people without symptoms for long periods of time, during which these agents can spread unnoticed to other patients in healthcare systems. The accurate identification of asymptomatic spreaders of AMRO in hospital settings is essential for supporting the design of interventions against healthcare-associated infections (HAIs). However, this task remains challenging because of limited observations of colonization and the complicated transmission dynamics occurring within hospitals and the broader community. Here, we study the transmission of methicillin-resistant Staphylococcus aureus (MRSA), a prevalent AMRO, in 66 Swedish hospitals and healthcare facilities with inpatients using a data-driven, agent-based model informed by deidentified real-world hospitalization records. Combining the transmission model, patient-to-patient contact networks, and sparse observations of colonization, we develop and validate an individual-level inference approach that estimates the colonization probability of individual hospitalized patients. For both model-simulated and historical outbreaks, the proposed method supports the more accurate identification of asymptomatic MRSA carriers than other traditional approaches. In addition, in silica control experiments indicate that interventions targeted to inpatients with a high-colonization probability outperform heuristic strategies informed by hospitalization history and contact tracing.

Efficient Bayesian inference of fully stochastic epidemiological models with applications to COVID-19

Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, Markov chain Monte Carlo sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.

Using Proper Mean Generation Intervals in Modeling of COVID-19

In susceptible-exposed-infectious-recovered (SEIR) epidemic models, with the exponentially distributed duration of exposed/infectious statuses, the mean generation interval (GI, time lag between infections of a primary case and its secondary case) equals the mean latent period (LP) plus the mean infectious period (IP). It was widely reported that the GI for COVID-19 is as short as 5 days. However, many works in top journals used longer LP or IP with the sum (i.e., GI), e.g., >7 days. This discrepancy will lead to overestimated basic reproductive number and exaggerated expectation of infection attack rate (AR) and control efficacy. We argue that it is important to use suitable epidemiological parameter values for proper estimation/prediction. Furthermore, we propose an epidemic model to assess the transmission dynamics of COVID-19 for Belgium, Israel, and the United Arab Emirates (UAE). We estimated a time-varying reproductive number [R0(t)] based on the COVID-19 deaths data and we found that Belgium has the highest AR followed by Israel and the UAE.

Estimating the generation interval and inferring the latent period of COVID-19 from the contact tracing data

The coronavirus disease 2019 (COVID-19) emerged by end of 2019, and became a serious public health threat globally in less than half a year. The generation interval and latent period, though both are of importance in understanding the features of COVID-19 transmission, are difficult to observe, and thus they can rarely be learnt from surveillance data empirically. In this study, we develop a likelihood framework to estimate the generation interval and incubation period simultaneously by using the contact tracing data of COVID-19 cases, and infer the pre-symptomatic transmission proportion and latent period thereafter. We estimate the mean of incubation period at 6.8 days (95 %CI: 6.2, 7.5) and SD at 4.1 days (95 %CI: 3.7, 4.8), and the mean of generation interval at 6.7 days (95 %CI: 5.4, 7.6) and SD at 1.8 days (95 %CI: 0.3, 3.8). The basic reproduction number is estimated ranging from 1.9 to 3.6, and there are 49.8 % (95 %CI: 33.3, 71.5) of the secondary COVID-19 infections likely due to pre-symptomatic transmission. Using the best estimates of model parameters, we further infer the mean latent period at 3.3 days (95 %CI: 0.2, 7.9). Our findings highlight the importance of both isolation for symptomatic cases, and for the pre-symptomatic and asymptomatic cases.

Model selection and parameter estimation for dynamic epidemic models via iterated filtering: application to rotavirus in Germany

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} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$R_0$\end{document} using these data.

The long-term changing dynamics of dengue infectivity in Guangdong, China, from 2008-2018: a modelling analysis

BACKGROUND

Dengue remains a severe threat to public health in tropical and subtropical regions. In China, over 85% of domestic dengue cases are in the Guangdong province and there were 53 139 reported cases during 2008-2018. In Guangdong, the 2014 dengue outbreak was the largest in the last 20 y and it was probably triggered by a new strain imported from other regions.

METHODS

We studied the long-term patterns of dengue infectivity in Guangdong from 2008-2018 and compared the infectivity estimates across different periods.

RESULTS

We found that the annual epidemics approximately followed exponential growth during 2011-2014. The transmission rates were at a low level during 2008-2012, significantly increased 1.43-fold [1.22, 1.69] during 2013-2014 and then decreased back to a low level after 2015. By using the mosquito index and the likelihood-inference approach, we found that the new strain most likely invaded Guangdong in April 2014.

CONCLUSIONS

The long-term changing dynamics of dengue infectivity are associated with the new dengue virus strain invasion and public health control programmes. The increase in infectiousness indicates the potential for dengue to go from being imported to becoming an endemic in Guangdong, China.

Synchronized nonpharmaceutical interventions for the control of COVID-19

The world is experiencing an ongoing pandemic of coronavirus disease-2019 (COVID-19), which is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In attempts to control the pandemic, a range of nonpharmaceutical interventions (NPIs) has been implemented worldwide. However, the effect of synchronized NPIs for the control of COVID-19 at temporal and spatial scales has not been well studied. Therefore, a meta-population model that incorporates essential nonlinear processes was constructed to uncover the transmission characteristics of SARS-CoV-2 and then assess the effectiveness of synchronized NPIs on COVID-19 dynamics in China. Regional synchronization of NPIs was observed in China, and it was found that a combination of synchronized NPIs (the travel restrictions, the social distancing and the infection isolation) prevented 93.7% of SARS-CoV-2 infections. The use of synchronized NPIs at the time of the Wuhan lockdown may have prevented as much as 38% of SARS-CoV-2 infections, compared with the unsynchronized scenario. The interconnectivity of the epicenter, the implementation time of synchronized NPIs, and the number of regions considered all affected the performance of synchronized NPIs. The results highlight the importance of using synchronized NPIs in high-risk regions for the control of COVID-19 and shed light on effective strategies for future pandemic responses.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11071-021-06505-0.

Inferring the Association between the Risk of COVID-19 Case Fatality and N501Y Substitution in SARS-CoV-2

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.

Epidemiological dynamics of enterovirus D68 in the United States and implications for acute flaccid myelitis

Acute flaccid myelitis (AFM) recently emerged in the United States as a rare but serious neurological condition since 2012. Enterovirus D68 (EV-D68) is thought to be a main causative agent, but limited surveillance of EV-D68 in the United States has hampered the ability to assess their causal relationship. Using surveillance data from the BioFire Syndromic Trends epidemiology network in the United States from January 2014 to September 2019, we characterized the epidemiological dynamics of EV-D68 and found latitudinal gradient in the mean timing of EV-D68 cases, which are likely climate driven. We also demonstrated a strong spatiotemporal association of EV-D68 with AFM. Mathematical modeling suggested that the recent dominant biennial cycles of EV-D68 dynamics may not be stable. Nonetheless, we predicted that a major EV-D68 outbreak, and hence an AFM outbreak, would have still been possible in 2020 under normal epidemiological conditions. Nonpharmaceutical intervention efforts due to the ongoing COVID-19 pandemic are likely to have reduced the sizes of EV-D68 and AFM outbreaks in 2020, illustrating the broader epidemiological impact of the pandemic.

COVID-19 dynamics considering the influence of hospital infrastructure: an investigation into Brazilian scenarios

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.