Functional law of large numbers for an epidemic model with random effects

Izyumtseva, Olga; KhudaBukhsh, Wasiur R.; Rempała, Grzegorz A.

Abstract

We consider the standard compartmental Susceptible-Infected-Recovered (SIR) model of infectious disease epidemiology with a random effect on the susceptibility of the individuals. We use a Continuous Time Markov Chain (CTMC) to model the dynamics of the population counts. We show that the scaled number of individuals in each compartment converges to a deterministic limit satisfying a system of Ordinary Differential Equations (ODEs), conditional on the random effect. Using the stochastic averaging principle for martingale problems, we derive a Functional Law of Large Numbers (FLLN) for the scaled process averaging out the random effect.

Citation

Izyumtseva, O., KhudaBukhsh, W. R., & Rempała, G. A. (2024). Functional law of large numbers for an epidemic model with random effects. In A. S. Srinivasa Rao, D. E. Martin, & C. Rao (Eds.), Modeling and Analysis of Longitudinal Data. Elsevier. https://doi.org/10.1016/bs.host.2024.07.002

• Online Publication Date: Sep 5, 2024
• Publication Date: Feb 11, 2024
• Deposit Date: Sep 12, 2024
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Series Title: Handbook of Statistics
• Series Number: 50
• Book Title: Modeling and Analysis of Longitudinal Data
• ISBN: 9780443136511
• DOI: https://doi.org/10.1016/bs.host.2024.07.002
• Public URL: https://nottingham-repository.worktribe.com/output/39461093
• Publisher URL: https://www.sciencedirect.com/science/article/abs/pii/S0169716124000294?via%3Dihub