Traveling wavefronts in diffusive cholera epidemic models with general incidence functions

Subir Dey, Tapan Kumar Kar and Toshikazu Kuniya

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 238-269

Abstract: This research investigates the dynamics of cholera epidemics using a reaction-diffusion framework that incorporates a generalized incidence function. The main focus is on whether traveling wave solutions (TWSs) exist or not and how they depend on two key threshold parameters: the basic reproduction number R0 of the associated ordinary differential equation (ODE) system and the minimal wave speed ν∗. Specifically, when R0>1, a minimal traveling wave speed ν∗ is identified. By employing the Schauder fixed point theorem, limiting arguments, and a Lyapunov function, we show the existence of a traveling wave connecting the disease-free and endemic equilibria for R0>1 and ν≥ν∗. Conversely, the non-existence of traveling waves is rigorously proven for R0≤1 and ν>0 by the comparison principle, and for R0>1 and 0<ν<ν∗ by the two-sided Laplace transform. Numerical simulations support the theoretical analysis, illustrating how diffusion and transmission rates influence the minimal wave speed and enhance our understanding of cholera’s spatial spread.

Keywords: Cholera model; Reaction-diffusion; Basic reproduction number; Minimal wave speed; Lyapunov function; Traveling wavefront (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:238-269

DOI: 10.1016/j.matcom.2025.07.020

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