Threshold dynamics of a reaction-advection-diffusion waterborne disease model with seasonality and human behavior change
Wei Wang, Xiaotong Wang, Xiaoting Fan
Abstract
To investigate the effects of environmental pollution and human behavior change on waterborne diseases, we propose a reaction-advection-diffusion waterborne disease model with a general boundary condition, which incorporates human hosts and reservoir aquatic of pathogen. We identify the basic reproduction number [Formula: see text] and discuss its asymptotic properties. We prove its threshold role: if [Formula: see text], the disease-free periodic solution is globally attractive; if [Formula: see text], the model system is uniformly persistent; if [Formula: see text], the disease-free steady state is globally asymptotically stable without the advection term, in which the proof is quite challenging due to human behavior change.