Global stability and asymptotic profiles of a partially degenerate reaction diffusion Cholera model with asymptomatic individuals

Considering the prevalence of asymptomatic individuals during the spread of disease, this article develops a model of degenerate reaction diffusion Cholera with asymptomatic individuals. First, the well-posedness of model is studied, including the global existence of solutions and the existence of attractor. Second, the basic reproduction number is defined to determine whether the disease is vanishing or persistent. In particular, we also analyze the asymptotic behavior of the endemic steady state when the diffusion rate of susceptible or asymptomatic individuals tends to 0 or infinity. Finally, by fitting the theoretical results with some numerical simulations, we find that the spatial distribution of disease and local epidemic risk are less affected by the mobility of susceptible populations, whereas the mobility of asymptomatic or symptomatic populations significantly affects the spatial and temporal distribution of infected populations. In addition, we found that the proportion of asymptomatic individuals to infected individuals is also a key factor in disease epidemics, and how to quickly diagnose asymptomatic individuals for disease control and prevention should be of a particular concern.