Spatial dynamics of a generalized cholera model with nonlocal time delay in a heterogeneous environment
Wei Wang, Xiaotong Wang, Hao Wang
Abstract
In this work, we mechanistically formulate a generalized cholera model with nonlocal time delay to study the impact of bacterial hyperinfectivity on cholera epidemics in a spatially heterogeneous environment. Mathematical challenges lie in the fact that (i) the generalized cholera model considers the intrinsic growth of short-lived hyperinfectious (HI vibrios) state of V. cholerae and lower-infectious (LI vibrios) state of V. cholerae simultaneously; and (ii) this article originally derives the detailed classifications of spatial dynamics for the cholera model with some generally functional response functions, non-uniformness of diffusion rates and nonlocal time delay. We introduce three basic reproduction numbers: one is for HI state of V. cholerae , the other is for LI state of V. cholerae , and another is for the cholera disease in the host population. Based on these basic reproduction numbers, we further establish the global threshold dynamics. Under some conditions, the basic reproduction number of infection is strictly decreasing with respect to the diffusion coefficients of infectious hosts.