Modeling Cholera Transmission Dynamics With Antibiotic Resistance and Mutation: A PDE Perspective

Cholera originated in the Ganges Delta of India in 1817 and then spread globally through several overlapping waves of epidemics. Its prevalence has since been reported to vary widely across different regions. Spatial heterogeneity plays a crucial role in shaping cholera transmission through the interplay of environment, population, and infrastructure. In this paper, we propose a new reaction-advection-diffusion equation model in a closed advective environment, which extends the ODE model introduced in Wang et al. (Wang W., Y. Lou, X. Wang, “Modeling Cholera Transmission Dynamics with Antibiotic Resistance and Mutation: A Case Study in Zimbabwe,” Mathematical Biosciences 390 (2025): 109545). We establish three critical thresholds and analyze the dependence of the basic reproduction number on model parameters by studying the principal eigenvalue of a series of cooperative elliptic systems with weight and potential. We further derive threshold-type results for the global dynamics, and investigate the asymptotic profiles of the coexistence endemic steady state when the diffusion rate of the susceptible individuals is small. Interestingly, for a spatially homogeneous case, we numerically find the spatially inhomogeneous steady state. We also observe that bacterial advection exhibits antibiotic-resistance-dependent effects on cholera outbreaks, and this dependence can be modified by environmental mutation of Vibrio cholerae. These results underscore the critical roles of antibiotic resistance and bacterial mutation in shaping spatial cholera transmission dynamics with geographical heterogeneity and population mobility.