Modeling pandemics

2025/08/20 by John F. Dawson, Dawson, John F., Fred Cooper +3
Computer Science · Mathematics · Medicine · #Applications (stat.AP) #COVID-19 epidemiological studies #Data Analysis with R #FOS: Computer and information sciences #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.2508.15125

openalex publication_date 2025/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review several models for pandemics that plagued the USA and the world in the past decade. Methods of data fitting are reviewed and several types of microscopic and rate equation models are discussed and numerically solved. This paper was written in March of 2021 and newer data is now available; however some of the models and techniques we used to numerically study these models are still of interest. Several appendices discuss in detail these models.

Citations

• Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions
• Universal Differential Equations for Scientific Machine Learning
• The construction of next-generation matrices for compartmental epidemic models
• A practical guide to stochastic simulations of reaction-diffusion processes
• Fourth-Order Time-Stepping for Stiff PDEs
• Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution
• Exponential Time Differencing for Stiff Systems
• A general method for numerically simulating the stochastic time evolution of coupled chemical reactions

Related

• Models for COVID-19 Pandemic: A Comparative Analysis
• Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus
• Data-driven modeling for different stages of pandemic response
• A universal generic description of the dynamics of the current COVID-19 pandemic
• On COVID-19 Modelling