Stochastic two-patch epidemic model with nonlinear recidivism

TL;DR

This paper introduces a stochastic two-patch epidemic model with nonlinear recidivism, revealing how randomness influences disease persistence, extinction, and oscillations in heterogeneous populations, extending deterministic frameworks.

Contribution

It develops a novel stochastic model incorporating nonlinear recidivism and analyzes stochastic effects on disease dynamics using multiple approximation methods.

Findings

Stochastic effects can lead to disease extinction and oscillations near critical thresholds.

Source-sink dynamics are observed, with one patch acting as a persistent source.

Numerical simulations demonstrate the impact of stochasticity on epidemic persistence.

Abstract

We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random transmission, recovery, and inter-patch movement fluctuations. We showcase the interplay between local dynamics and migration effects on disease persistence using Monte Carlo simulations and three stochastic approximations-discrete-time Markov chain (DTMC), Poisson, and stochastic differential equations (SDE). Our analysis shows that stochastic effects can cause extinction events and oscillations near critical thresholds like the basic reproduction number, R0, phenomena absent in deterministic models. Numerical simulations highlight source-sink dynamics, where one patch is a persistent infection source while the other experiences intermittent outbreaks.