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Kiss IZ, Berthouze L, KhudaBukhsh WR. Towards Inferring Network Properties from Epidemic Data. Bull Math Biol 2023; 86:6. [PMID: 38063898 PMCID: PMC10709280 DOI: 10.1007/s11538-023-01235-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 11/09/2023] [Indexed: 12/18/2023]
Abstract
Epidemic propagation on networks represents an important departure from traditional mass-action models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using mean-field models, such as the pairwise model (PWM), the high-dimensionality becomes tractable. While such models have been used extensively for model analysis, there is limited work in the context of statistical inference. In this paper, we explore the extent to which the PWM with the susceptible-infected-recovered (SIR) epidemic can be used to infer disease- and network-related parameters. Data from an epidemics can be loosely categorised as being population level, e.g., daily new cases, or individual level, e.g., recovery times. To understand if and how network inference is influenced by the type of data, we employed the widely-used MLE approach for population-level data and dynamical survival analysis (DSA) for individual-level data. For scenarios in which there is no model mismatch, such as when data are generated via simulations, both methods perform well despite strong dependence between parameters. In contrast, for real-world data, such as foot-and-mouth, H1N1 and COVID19, whereas the DSA method appears fairly robust to potential model mismatch and produces parameter estimates that are epidemiologically plausible, our results with the MLE method revealed several issues pertaining to parameter unidentifiability and a lack of robustness to exact knowledge about key quantities such as population size and/or proportion of under reporting. Taken together, however, our findings suggest that network-based mean-field models can be used to formulate approximate likelihoods which, coupled with an efficient inference scheme, make it possible to not only learn about the parameters of the disease dynamics but also that of the underlying network.
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Affiliation(s)
- Istvan Z Kiss
- Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9QH, UK.
- Network Science Institute, Northeastern University London, London, E1W 1LP, UK.
| | - Luc Berthouze
- Department of Informatics, University of Sussex, Falmer, Brighton, BN1 9QH, UK
| | - Wasiur R KhudaBukhsh
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
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2
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KhudaBukhsh WR, Khalsa SK, Kenah E, Rempała GA, Tien JH. COVID-19 dynamics in an Ohio prison. Front Public Health 2023; 11:1087698. [PMID: 37064663 PMCID: PMC10098107 DOI: 10.3389/fpubh.2023.1087698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Accepted: 02/20/2023] [Indexed: 03/31/2023] Open
Abstract
Incarcerated individuals are a highly vulnerable population for infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Understanding the transmission of respiratory infections within prisons and between prisons and surrounding communities is a crucial component of pandemic preparedness and response. Here, we use mathematical and statistical models to analyze publicly available data on the spread of SARS-CoV-2 reported by the Ohio Department of Rehabilitation and Corrections (ODRC). Results from mass testing conducted on April 16, 2020 were analyzed together with time of first reported SARS-CoV-2 infection among Marion Correctional Institution (MCI) inmates. Extremely rapid, widespread infection of MCI inmates was reported, with nearly 80% of inmates infected within 3 weeks of the first reported inmate case. The dynamical survival analysis (DSA) framework that we use allows the derivation of explicit likelihoods based on mathematical models of transmission. We find that these data are consistent with three non-exclusive possibilities: (i) a basic reproduction number >14 with a single initially infected inmate, (ii) an initial superspreading event resulting in several hundred initially infected inmates with a reproduction number of approximately three, or (iii) earlier undetected circulation of virus among inmates prior to April. All three scenarios attest to the vulnerabilities of prisoners to COVID-19, and the inability to distinguish among these possibilities highlights the need for improved infection surveillance and reporting in prisons.
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Affiliation(s)
- Wasiur R. KhudaBukhsh
- School of Mathematical Sciences, The University of Nottingham, Nottingham, United Kingdom
| | - Sat Kartar Khalsa
- Wexner Medical Center, The Ohio State University, Columbus, OH, United States
| | - Eben Kenah
- Division of Biostatistics, The Ohio State University, Columbus, OH, United States
| | - Gregorz A. Rempała
- Division of Biostatistics, Department of Mathematics, The Ohio State University, Columbus, OH, United States
| | - Joseph H. Tien
- Division of Epidemiology, Department of Mathematics, The Ohio State University, Columbus, OH, United States
- *Correspondence: Joseph H. Tien
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KhudaBukhsh WR, Bastian CD, Wascher M, Klaus C, Sahai SY, Weir MH, Kenah E, Root E, Tien JH, Rempała GA. Projecting COVID-19 cases and hospital burden in Ohio. J Theor Biol 2023; 561:111404. [PMID: 36627078 PMCID: PMC9824941 DOI: 10.1016/j.jtbi.2022.111404] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Revised: 12/13/2022] [Accepted: 12/26/2022] [Indexed: 01/09/2023]
Abstract
As the Coronavirus 2019 disease (COVID-19) started to spread rapidly in the state of Ohio, the Ecology, Epidemiology and Population Health (EEPH) program within the Infectious Diseases Institute (IDI) at The Ohio State University (OSU) took the initiative to offer epidemic modeling and decision analytics support to the Ohio Department of Health (ODH). This paper describes the methodology used by the OSU/IDI response modeling team to predict statewide cases of new infections as well as potential hospital burden in the state. The methodology has two components: (1) A Dynamical Survival Analysis (DSA)-based statistical method to perform parameter inference, statewide prediction and uncertainty quantification. (2) A geographic component that down-projects statewide predicted counts to potential hospital burden across the state. We demonstrate the overall methodology with publicly available data. A Python implementation of the methodology is also made publicly available. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".
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Affiliation(s)
- Wasiur R KhudaBukhsh
- School of Mathematical Sciences, University of Nottingham, University Park Nottingham NG7 2RD, United Kingdom.
| | - Caleb Deen Bastian
- Program in Applied and Computational Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA.
| | - Matthew Wascher
- Department of Mathematics, University of Dayton, 300 College Park, Dayton, OH 45469, USA.
| | - Colin Klaus
- Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Avenue, Columbus, OH 43210, USA; College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA; Infectious Diseases Institute, 208 Bricker Hall, 190 North Oval Mall, Columbus, OH 43210-1358, USA.
| | - Saumya Yashmohini Sahai
- Department of Computer Science and Engineering, The Ohio State University, 395 Dreese Laboratories, 2015 Neil Avenue, Columbus, OH 43210, USA.
| | - Mark H Weir
- College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA; Infectious Diseases Institute, 208 Bricker Hall, 190 North Oval Mall, Columbus, OH 43210-1358, USA; The Sustainability Institute, The Ohio State University, 74 W. 18th Avenue, Columbus, OH 43210, USA.
| | - Eben Kenah
- College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA; Infectious Diseases Institute, 208 Bricker Hall, 190 North Oval Mall, Columbus, OH 43210-1358, USA.
| | - Elisabeth Root
- Institute for Disease Modeling, The Bill & Melinda Gates Foundation, Seattle, WA, USA.
| | - Joseph H Tien
- Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Avenue, Columbus, OH 43210, USA; College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA; Infectious Diseases Institute, 208 Bricker Hall, 190 North Oval Mall, Columbus, OH 43210-1358, USA; Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210-1174, USA.
| | - Grzegorz A Rempała
- Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Avenue, Columbus, OH 43210, USA; College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA; Infectious Diseases Institute, 208 Bricker Hall, 190 North Oval Mall, Columbus, OH 43210-1358, USA; Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210-1174, USA.
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Klaus C, Wascher M, KhudaBukhsh WR, Rempała GA. Likelihood-Free Dynamical Survival Analysis applied to the COVID-19 epidemic in Ohio. Math Biosci Eng 2023; 20:4103-4127. [PMID: 36899619 DOI: 10.3934/mbe.2023192] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The Dynamical Survival Analysis (DSA) is a framework for modeling epidemics based on mean field dynamics applied to individual (agent) level history of infection and recovery. Recently, the Dynamical Survival Analysis (DSA) method has been shown to be an effective tool in analyzing complex non-Markovian epidemic processes that are otherwise difficult to handle using standard methods. One of the advantages of Dynamical Survival Analysis (DSA) is its representation of typical epidemic data in a simple although not explicit form that involves solutions of certain differential equations. In this work we describe how a complex non-Markovian Dynamical Survival Analysis (DSA) model may be applied to a specific data set with the help of appropriate numerical and statistical schemes. The ideas are illustrated with a data example of the COVID-19 epidemic in Ohio.
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Affiliation(s)
- Colin Klaus
- Mathematical Biosciences Institute and the Division of Biostatistics, College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA
| | - Matthew Wascher
- Department of Mathematics, University of Dayton, 300 College Park Dayton, Ohio 45469, USA
| | - Wasiur R KhudaBukhsh
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, UK
| | - Grzegorz A Rempała
- Mathematical Biosciences Institute and the Division of Biostatistics, College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA
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Cui K, KhudaBukhsh WR, Koeppl H. Hypergraphon mean field games. Chaos 2022; 32:113129. [PMID: 36456333 DOI: 10.1063/5.0093758] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 10/24/2022] [Indexed: 06/17/2023]
Abstract
We propose an approach to modeling large-scale multi-agent dynamical systems allowing interactions among more than just pairs of agents using the theory of mean field games and the notion of hypergraphons, which are obtained as limits of large hypergraphs. To the best of our knowledge, ours is the first work on mean field games on hypergraphs. Together with an extension to a multi-layer setup, we obtain limiting descriptions for large systems of non-linear, weakly interacting dynamical agents. On the theoretical side, we prove the well-foundedness of the resulting hypergraphon mean field game, showing both existence and approximate Nash properties. On the applied side, we extend numerical and learning algorithms to compute the hypergraphon mean field equilibria. To verify our approach empirically, we consider a social rumor spreading model, where we give agents intrinsic motivation to spread rumors to unaware agents, and an epidemic control problem.
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Affiliation(s)
- Kai Cui
- Technische Universität Darmstadt, 64283 Darmstadt, Germany
| | - Wasiur R KhudaBukhsh
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom
| | - Heinz Koeppl
- Technische Universität Darmstadt, 64283 Darmstadt, Germany
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KhudaBukhsh WR, Bastian CD, Wascher M, Klaus C, Sahai SY, Weir M, Kenah E, Root E, Tien JH, Rempala G. Projecting COVID-19 Cases and Subsequent Hospital Burden in Ohio. medRxiv 2022:2022.07.27.22278117. [PMID: 35923319 PMCID: PMC9347277 DOI: 10.1101/2022.07.27.22278117] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Abstract
As the Coronavirus 2019 (COVID-19) disease started to spread rapidly in the state of Ohio, the Ecology, Epidemiology and Population Health (EEPH) program within the Infectious Diseases Institute (IDI) at the Ohio State University (OSU) took the initiative to offer epidemic modeling and decision analytics support to the Ohio Department of Health (ODH). This paper describes the methodology used by the OSU/IDI response modeling team to predict statewide cases of new infections as well as potential hospital burden in the state. The methodology has two components: 1) A Dynamic Survival Analysis (DSA)-based statistical method to perform parameter inference, statewide prediction and uncertainty quantification. 2) A geographic component that down-projects statewide predicted counts to potential hospital burden across the state. We demonstrate the overall methodology with publicly available data. A Python implementation of the methodology has been made available publicly. Highlights We present a novel statistical approach called Dynamic Survival Analysis (DSA) to model an epidemic curve with incomplete data. The DSA approach is advantageous over standard statistical methods primarily because it does not require prior knowledge of the size of the susceptible population, the overall prevalence of the disease, and also the shape of the epidemic curve.The principal motivation behind the study was to obtain predictions of case counts of COVID-19 and the resulting hospital burden in the state of Ohio during the early phase of the pandemic.The proposed methodology was applied to the COVID-19 incidence data in the state of Ohio to support the Ohio Department of Health (ODH) and the Ohio Hospital Association (OHA) with predictions of hospital burden in each of the Hospital Catchment Areas (HCAs) of the state.
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Affiliation(s)
- Wasiur R. KhudaBukhsh
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Caleb Deen Bastian
- Applied Mathematics, Princeton University and Massive Dynamics, Princeton, NJ, USA
| | - Matthew Wascher
- Department of Mathematics, University of Dayton, 300 College Park, Dayton, Ohio 45469, USA
| | - Colin Klaus
- Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Avenue, Columbus OH 43210, USA
- College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA
- Infectious Diseases Institute, 208 Bricker Hall, 190 North Oval Mall, Columbus, OH 43210-1358, USA
| | - Saumya Yashmohini Sahai
- Department of Computer Science and Engineering, The Ohio State University, 395 Dreese Laboratories, 2015 Neil Avenue, Columbus, OH 43210, USA
| | - Mark Weir
- College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA
- Infectious Diseases Institute, 208 Bricker Hall, 190 North Oval Mall, Columbus, OH 43210-1358, USA
- The Sustainability Institute, The Ohio State University, 74 W. 18th Avenue, Columbus, OH 43210, USA
| | - Eben Kenah
- College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA
- Infectious Diseases Institute, 208 Bricker Hall, 190 North Oval Mall, Columbus, OH 43210-1358, USA
| | - Elisabeth Root
- Institute for Disease Modeling, The Bill & Melinda Gates Foundation, Seattle, Washington, USA
| | - Joseph H. Tien
- Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Avenue, Columbus OH 43210, USA
- College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA
- Infectious Diseases Institute, 208 Bricker Hall, 190 North Oval Mall, Columbus, OH 43210-1358, USA
- Department of Mathematics, The Ohio State University, 231 West 18th Avenue Columbus, OH 43210-1174, USA
| | - Grzegorz Rempala
- Mathematical Biosciences Institute, The Ohio State University, 1735 Neil Avenue, Columbus OH 43210, USA
- College of Public Health, The Ohio State University, Cunz Hall, 1841 Neil Avenue, Columbus, OH 43210, USA
- Infectious Diseases Institute, 208 Bricker Hall, 190 North Oval Mall, Columbus, OH 43210-1358, USA
- Department of Mathematics, The Ohio State University, 231 West 18th Avenue Columbus, OH 43210-1174, USA
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Abstract
We present a new method for analysing stochastic epidemic models under minimal assumptions. The method, dubbed dynamic survival analysis (DSA), is based on a simple yet powerful observation, namely that population-level mean-field trajectories described by a system of partial differential equations may also approximate individual-level times of infection and recovery. This idea gives rise to a certain non-Markovian agent-based model and provides an agent-level likelihood function for a random sample of infection and/or recovery times. Extensive numerical analyses on both synthetic and real epidemic data from foot-and-mouth disease in the UK (2001) and COVID-19 in India (2020) show good accuracy and confirm the method’s versatility in likelihood-based parameter estimation. The accompanying software package gives prospective users a practical tool for modelling, analysing and interpreting epidemic data with the help of the DSA approach.
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Affiliation(s)
| | | | - István Z Kiss
- Department of Mathematics, University of Sussex, Brighton, BN1 9RH, UK
| | - Eben Kenah
- Department of Biostatistics, The Ohio State University, Columbus, OH 43210, USA
| | - Max Jensen
- Department of Mathematics, University of Sussex, Brighton, BN1 9RH, UK
| | - Grzegorz A Rempała
- Department of Biostatistics, The Ohio State University, Columbus, OH 43210, USA
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8
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Klaus C, Wascher M, KhudaBukhsh WR, Tien JH, Rempała GA, Kenah E. Assortative mixing among vaccination groups and biased estimation of reproduction numbers. Lancet Infect Dis 2022; 22:579-581. [PMID: 35460647 PMCID: PMC9020805 DOI: 10.1016/s1473-3099(22)00155-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/19/2021] [Revised: 02/10/2022] [Accepted: 02/23/2022] [Indexed: 06/14/2023]
Affiliation(s)
- Colin Klaus
- The Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, USA; Biostatistics Division, College of Public Health, The Ohio State University, Columbus, OH 43210, USA
| | - Matthew Wascher
- Department of Mathematics, University of Dayton, Dayton, OH, USA
| | | | - Joseph H Tien
- Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA
| | - Grzegorz A Rempała
- Biostatistics Division, College of Public Health, The Ohio State University, Columbus, OH 43210, USA; Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA
| | - Eben Kenah
- Biostatistics Division, College of Public Health, The Ohio State University, Columbus, OH 43210, USA.
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Cui K, KhudaBukhsh WR, Koeppl H. Motif-based mean-field approximation of interacting particles on clustered networks. Phys Rev E 2022; 105:L042301. [PMID: 35590665 DOI: 10.1103/physreve.105.l042301] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Accepted: 04/07/2022] [Indexed: 06/15/2023]
Abstract
Interacting particles on graphs are routinely used to study magnetic behavior in physics, disease spread in epidemiology, and opinion dynamics in social sciences. The literature on mean-field approximations of such systems for large graphs typically remains limited to specific dynamics, or assumes cluster-free graphs for which standard approximations based on degrees and pairs are often reasonably accurate. Here, we propose a motif-based mean-field approximation that considers higher-order subgraph structures in large clustered graphs. Numerically, our equations agree with stochastic simulations where existing methods fail.
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Affiliation(s)
- Kai Cui
- Department of Electrical Engineering and Information Technology, Technische Universität Darmstadt, 64287 Darmstadt, Germany
| | | | - Heinz Koeppl
- Department of Electrical Engineering and Information Technology, Technische Universität Darmstadt, 64287 Darmstadt, Germany
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Somekh I, KhudaBukhsh WR, Root ED, Boker LK, Rempala G, Simões EAF, Somekh E. Quantifying the Population-level Effect of the COVID-19 Mass Vaccination Campaign in Israel: a Modeling Study. Open Forum Infect Dis 2022; 9:ofac087. [PMID: 35493128 PMCID: PMC9043004 DOI: 10.1093/ofid/ofac087] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2021] [Accepted: 02/16/2022] [Indexed: 11/28/2022] Open
Abstract
Background Estimating real-world vaccine effectiveness is challenging as a variety of population factors can impact vaccine effectiveness. We aimed to assess the population-level reduction in cumulative severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) cases, hospitalizations, and mortality due to the BNT162b2 mRNA coronavirus disease 2019 (COVID-19) vaccination campaign in Israel during January–February 2021. Methods A susceptible-infected-recovered/removed (SIR) model and a Dynamic Survival Analysis (DSA) statistical approach were used. Daily counts of individuals who tested positive and of vaccine doses administered, obtained from the Israeli Ministry of Health, were used to calibrate the model. The model was parameterized using values derived from a previous phase of the pandemic during which similar lockdown and other preventive measures were implemented in order to take into account the effect of these prevention measures on COVID-19 spread. Results Our model predicted for the total population a reduction of 648 585 SARS-CoV-2 cases (75% confidence interval [CI], 25 877–1 396 963) during the first 2 months of the vaccination campaign. The number of averted hospitalizations for moderate to severe conditions was 16 101 (75% CI, 2010–33 035), and reduction of death was estimated at 5123 (75% CI, 388–10 815) fatalities. Among children aged 0–19 years, we estimated a reduction of 163 436 (75% CI, 0–433 233) SARS-CoV-2 cases, which we consider to be an indirect effect of the vaccine. Conclusions Our results suggest that the rapid vaccination campaign prevented hundreds of thousands of new cases as well as thousands of hospitalizations and fatalities and has probably averted a major health care crisis.
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Affiliation(s)
- Ido Somekh
- Department of Pediatric Hematology Oncology, Schneider Children’s Medical Center of Israel, Petah Tikva, Israel
- Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
| | - Wasiur R KhudaBukhsh
- School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| | - Elisabeth Dowling Root
- Department of Geography and Division of Epidemiology, The Ohio State University, and Translational Data Analytics Institute Columbus, Columbus, OH, USA
| | - Lital Keinan Boker
- Israel Center for Disease Control, Israel Ministry of Health, Israel
- School of Public Health, University of Haifa, Haifa, Israel
| | - Grzegorz Rempala
- Department of Mathematics, The Ohio State University, Columbus, OH, USA
| | | | - Eli Somekh
- Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
- Department of Pediatrics, Mayanei Hayeshuah Medical Center, Bnei Brak, Israel
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Sahai SY, Gurukar S, KhudaBukhsh WR, Parthasarathy S, Rempała GA. A machine learning model for nowcasting epidemic incidence. Math Biosci 2021; 343:108677. [PMID: 34848217 PMCID: PMC8635898 DOI: 10.1016/j.mbs.2021.108677] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2021] [Revised: 07/18/2021] [Accepted: 07/18/2021] [Indexed: 11/07/2022]
Abstract
Due to delay in reporting, the daily national and statewide COVID-19 incidence counts are often unreliable and need to be estimated from recent data. This process is known in economics as nowcasting. We describe in this paper a simple random forest statistical model for nowcasting the COVID-19 daily new infection counts based on historic data along with a set of simple covariates, such as the currently reported infection counts, day of the week, and time since first reporting. We apply the model to adjust the daily infection counts in Ohio, and show that the predictions from this simple data-driven method compare favorably both in quality and computational burden to those obtained from the state-of-the-art hierarchical Bayesian model employing a complex statistical algorithm. The interactive notebook for performing nowcasting is available online at https://tinyurl.com/simpleMLnowcasting.
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Affiliation(s)
- Saumya Yashmohini Sahai
- Department of Computer Science and Engineering, The Ohio State University, United States of America.
| | - Saket Gurukar
- Department of Computer Science and Engineering, The Ohio State University, United States of America
| | - Wasiur R KhudaBukhsh
- Division of Biostatistics and Mathematical Biosciences Institute, The Ohio State University, United States of America
| | - Srinivasan Parthasarathy
- Department of Computer Science and Engineering, The Ohio State University, United States of America
| | - Grzegorz A Rempała
- Division of Biostatistics and Mathematical Biosciences Institute, The Ohio State University, United States of America.
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Abstract
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have been used widely. However, some biophysical processes such as gene transcription and translation are known to have a significant gap between the initiation and the completion of the processes, which renders the usual assumption of exponential distribution untenable. In this paper, we consider relaxing this assumption by incorporating age-dependent random time delays (distributed according to a given probability distribution) into the system dynamics. We do so by constructing a measure-valued Markov process on a more abstract state space, which allows us to keep track of the 'ages' of molecules participating in a chemical reaction. We study the large-volume limit of such age-structured systems. We show that, when appropriately scaled, the stochastic system can be approximated by a system of partial differential equations (PDEs) in the large-volume limit, as opposed to ordinary differential equations (ODEs) in the classical theory. We show how the limiting PDE system can be used for the purpose of further model reductions and for devising efficient simulation algorithms. In order to describe the ideas, we use a simple transcription process as a running example. We, however, note that the methods developed in this paper apply to a wide class of biophysical systems.
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Affiliation(s)
- Wasiur R KhudaBukhsh
- Mathematical Biosciences Institute and the College of Public Health, The Ohio State University, 1735 Neil Avenue, Columbus OH 43210, United States of America
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13
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KhudaBukhsh WR, Choi B, Kenah E, Rempała GA. Survival dynamical systems: individual-level survival analysis from population-level epidemic models. Interface Focus 2019; 10:20190048. [PMID: 31897290 PMCID: PMC6936005 DOI: 10.1098/rsfs.2019.0048] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/07/2019] [Indexed: 12/20/2022] Open
Abstract
In this paper, we show that solutions to ordinary differential equations describing the large-population limits of Markovian stochastic epidemic models can be interpreted as survival or cumulative hazard functions when analysing data on individuals sampled from the population. We refer to the individual-level survival and hazard functions derived from population-level equations as a survival dynamical system (SDS). To illustrate how population-level dynamics imply probability laws for individual-level infection and recovery times that can be used for statistical inference, we show numerical examples based on synthetic data. In these examples, we show that an SDS analysis compares favourably with a complete-data maximum-likelihood analysis. Finally, we use the SDS approach to analyse data from a 2009 influenza A(H1N1) outbreak at Washington State University.
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Affiliation(s)
- Wasiur R KhudaBukhsh
- Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA
| | - Boseung Choi
- Division of Economics and Statistics, Department of National Statistics, Korea University Sejong campus, Sejong Special Autonomous City, Republic of Korea
| | - Eben Kenah
- Division of Biostatistics, College of Public Health, The Ohio State University, Columbus, OH, USA
| | - Grzegorz A Rempała
- Division of Biostatistics, College of Public Health and Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA
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14
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Choi B, Busch S, Kazadi D, Ilunga B, Okitolonda E, Dai Y, Lumpkin R, Saucedo O, KhudaBukhsh WR, Tien J, Yotebieng M, Kenah E, Rempala GA. Modeling outbreak data: Analysis of a 2012 Ebola virus disease epidemic in DRC. Biomath (Sofia) 2019; 8:1910037. [PMID: 33192155 PMCID: PMC7665115 DOI: 10.11145/j.biomath.2019.10.037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We describe two approaches to modeling data from a small to moderate-sized epidemic outbreak. The first approach is based on a branching process approximation and direct analysis of the transmission network, whereas the second one is based on a survival model derived from the classical SIR equations with no explicit transmission information. We compare these approaches using data from a 2012 outbreak of Ebola virus disease caused by Bundibugyo ebolavirus in city of Isiro, Democratic Republic of the Congo. The branching process model allows for a direct comparison of disease transmission across different environments, such as the general community or the Ebola treatment unit. However, the survival model appears to yield parameter estimates with more accuracy and better precision in some circumstances.
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Affiliation(s)
- Boseung Choi
- Department of National Statistics, Korea University Sejoung Campus Sejoung, Republic of Korea
| | - Sydney Busch
- Department of Mathematics, Augsburg College Minneapolis, MN, USA
| | - Dieudonné Kazadi
- Ministry of Health, Democratic Republic of the Congo
- School of Public Health, University of Kinshasa Kinshasa, Democratic Republic of the Congo
| | - Benoit Ilunga
- School of Public Health, University of Kinshasa Kinshasa, Democratic Republic of the Congo
| | | | - Yi Dai
- Division of Biostatistics, College of Public Health, The Ohio State University, Columbus, OH, USA
| | - Robert Lumpkin
- Department of Mathematics, The Ohio State University, Columbus, OH, USA
| | - Omar Saucedo
- Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA
| | - Wasiur R. KhudaBukhsh
- Division of Biostatistics, College of Public Health, The Ohio State University, Columbus, OH, USA
- Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA
| | - Joseph Tien
- Department of Mathematics, The Ohio State University, Columbus, OH, USA
| | - Marcel Yotebieng
- Division of Epidemiology, College of Public Health, The Ohio State University, Columbus, OH, USA
| | - Eben Kenah
- Division of Biostatistics, College of Public Health, The Ohio State University, Columbus, OH, USA
| | - Grzegorz A. Rempala
- Division of Biostatistics, College of Public Health, The Ohio State University, Columbus, OH, USA
- Department of Mathematics, The Ohio State University, Columbus, OH, USA
- Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA
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15
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KhudaBukhsh WR, Kar S, Rizk A, Koeppl H. Provisioning and Performance Evaluation of Parallel Systems with Output Synchronization. ACM Trans Model Perform Eval Comput Syst 2019. [DOI: 10.1145/3300142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Abstract
Parallel server frameworks are widely deployed in modern large-data processing applications. Intuitively, splitting and parallel processing of the workload provides accelerated application response times and scaling flexibility. Examples of such frameworks include MapReduce, Hadoop, and Spark. For many applications, the dynamics of such systems are naturally captured by a Fork-Join (FJ) queuing model, where incoming jobs are split into tasks each of which is mapped to exactly one server. When all the tasks that belong to one job are executed, the job is reassembled and leaves the system. We consider this behavior at the output as a synchronization constraint.
In this article, we study the performance of such parallel systems for different server properties, e.g., work-conservingness, phase-type behavior, and as suggested by recent evidence, for bursty input job arrivals. We establish a Large Deviations Principle for the steady-state job waiting times in an FJ system based on Markov-additive processes. Building on that, we present a performance analysis framework for FJ systems and provide computable bounds on the tail probabilities of the steady-state waiting times. We validate our bounds using estimates obtained through simulations. In addition, we define and analyze provisioning, a flexible division of jobs into tasks, in FJ systems. Finally, we use this framework together with real-world traces to show the benefits of an adaptive provisioning system that adjusts the service within an FJ system based on the arrival intensity.
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Affiliation(s)
| | - Sounak Kar
- Technische Universität Darmstadt, Germany
| | - Amr Rizk
- Technische Universität Darmstadt, Germany
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