Likelihood-Free Dynamical Survival Analysis applied to the COVID-19 epidemic in Ohio

Colin Klaus; Matthew Wascher; Wasiur R. KhudaBukhsh; Grzegorz A. Rempała; Colin Klaus; Matthew Wascher; Wasiur R. KhudaBukhsh; Grzegorz A. Rempała

doi:10.3934/mbe.2023192

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 4103-4127. doi: 10.3934/mbe.2023192

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Research article Special Issues

Likelihood-Free Dynamical Survival Analysis applied to the COVID-19 epidemic in Ohio

1.
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
2.
Department of Mathematics, University of Dayton, 300 College Park Dayton, Ohio 45469, USA
3.
School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, UK

Received: 19 September 2022 Revised: 09 December 2022 Accepted: 12 December 2022 Published: 20 December 2022

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.
- SIR epidemics,
- vaccination,
- PDE system,
- nonlocal PDE,
- nonlocal conservation laws,
- ABC method,
- statistical inference,
- numerical solution
Citation: Colin Klaus, Matthew Wascher, Wasiur R. KhudaBukhsh, Grzegorz A. Rempała. Likelihood-Free Dynamical Survival Analysis applied to the COVID-19 epidemic in Ohio[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 4103-4127. doi: 10.3934/mbe.2023192

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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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