Dynamical Survival Analysis for Epidemic Modeling

Grzegorz A. Rempała () and Wasiur R. KhudaBukhsh ()
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Grzegorz A. Rempała: The Ohio State University, Division of Biostatistics
Wasiur R. KhudaBukhsh: The University of Nottingham, School of Mathematical Sciences

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 1481-1497 from Springer

Abstract: Abstract This chapter describes the dynamical survival analysis (DSA) method for modeling infectious diseases. This method provides a powerful framework for analyzing compartmental models of large epidemics, such as the popular susceptible-infected-recovered (SIR) model. In the DSA framework, traditional SIR mean-field differential equations are interpreted in terms of population infectious pressure instead of average infection counts. This simplifies statistical inference for the epidemic process parameters, allowing for top-down analysis of the epidemic data using the mass transfer model based on lumping of the individual-based SIR stochastic model. The individual dynamics of infections are often approximately independent in large populations, which further simplifies the approach according to the propagation of chaos principle. The chapter summarizes the general principles of DSA and includes a small numerical example that illustrates the statistical inference procedure for SIR models using the new framework.

Keywords: SIR model; Dynamical system; Lumpable Markov process; Agent-based model; Survival function; Mass transfer model; Statistical inference; Likelihood function; Multinomial distribution; Markov chain Monte Carlo (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16368-4_31

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