Threshold dynamics of a reaction-advection-diffusion waterborne disease model with seasonality and human behavior change

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 Script capital R-0 and discuss its asymptotic properties. We prove its threshold role: if Script capital R-0 < 1, the disease-free periodic solution is globally attractive; if Script capital R-0 > 1, the model system is uniformly persistent; if Script capital R-0 = 1, 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.