Stochastic models of infectious diseases in a periodic environment with application to cholera epidemics (Q2022092)

This paper studies stochastic models for a choler epidemic using a general deterministic infectious disease framework in a periodic environment. To explore the seasonal dynamics of disease outbreaks in epidemic models with periodic parameters, the paper applies multi-type branching process approximation as well as backward Kolmogorov differential equations. The paper derives approximations for the mean and variance of the first extinction time given the occurrence of an extinction. Approximations have also been done for epidemics with seasonality in the direct and indirect transmission rates as well as shedding rate. The results are validated through numerical simulations of time-inhomogeneous Markov processes in cholera epidemics.