Spatiotemporal cholera dynamics with antibiotic resistance and vaccination via demographic-epidemic data in Zimbabwe

Abstract

The diffusion of cholera epidemics and the emergence of drug-resistant strain pose significant challenges to cholera control and treatment, emphasizing the need for more effective interventions. By establishing a reaction-diffusion model of cholera with vaccination and two strains (wild and drug-resistant), we study the spatiotemporal dynamics of cholera transmission in this paper. In a spatially heterogeneous case, we derive $R_0$ and establish a threshold result: the disease-free steady state is globally stable if $R_0<1$ , and the disease persists if $R_0>1$ . In addition, we prove the global stability of the endemic equilibrium by constructing a Lyapunov functional in a spatially homogeneous case. Our model is successfully validated by the cholera data in Zimbabwe via Markov Chain Monte Carlo (MCMC). Using COMSOL Multiphysics software, we display the spatial transmission of cholera in the two-dimensional geographic map via demographic data in Zimbabwe. This offers a novel perspective for investigating the spatiotemporal dynamics of cholera transmission. Our findings indicate that restricted local population diffusion may contribute to the persistence and localized transmission of cholera in certain regions of Zimbabwe. Simulations further indicate that vaccination can serve as an effective intervention under such spatial dynamics.

Keywords: Cholera; Markov Chain Monte Carlo (MCMC); demographic-epidemic data; reaction-diffusion model; spatiotemporal dynamics.