Epidemic dynamics and spatial segregation driven by cognitive diffusion and nonlinear incidence

We propose susceptible-infected-susceptible epidemic reaction–diffusion models with cognitive movement and nonlinear incidence $S^q{I}^p$ $(p,q>0)$ in a spatially heterogeneous environment. The cognitive dispersal term takes either random diffusion or symmetric diffusion. Building upon the $L^{\infty }$-estimates of positive solutions under $p,q>0$, we state the asymptotic dynamics for , $q>0$. The numerical results reveal spatial segregation of susceptible and infected populations: (a) the heterogeneous random diffusion can segregate the population and reduce the infection fraction significantly; (b) the segregation phenomenon disappears as the ratio $p/q$ approaches one from below; (c) the disease-free region strengthens the segregation induced by heterogeneous random diffusion; (d) the segregation governed by random diffusion is more sensitive to the incidence mechanism; (e) the distribution of steady states driven by symmetric diffusion is always similar to that by homogeneous diffusion.