2024/05/16 by Juan G. Calvo, Mario Ignacio Simoy, Calvo, Juan G. +7
Mathematics · Medicine · Physics and Astronomy · #60H15 #60J20 #92-08 #92D30 #COVID-19 epidemiological studies #Complex Network Analysis Techniques #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.2405.10998
openalex publication_date 2024/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.