In this paper, we proposed a susceptible-infected-susceptible (SIS) reaction–diffusion model with spatial and behavioral heterogeneity. We established the basic reproduction number \(R_0\) based on the next generation infection operators and then derived the threshold dynamics in terms of \(R_0\) . We obtained the monotonicity of \(R_0\) and its asymptotic properties as diffusion rates of the infected individuals approach zero or infinity. In particular, the basic reproduction number \(R_0\) decreases with increasing diffusion rates of the infected individuals given the balance of transition from adopting normal to altered behaviors and from altered to normal behaviors, which agrees well with the existing conclusion. Interestingly, \(R_0\) may increase or exhibit non-monotonicity with increasing diffusion rate for non-balanced transition of different behaviors. Further, we numerically examined the effect of behavior changes on \(R_0\) and main results reveal that increasing transition rate from normal to altered behaviors may either decrease or increase \(R_0\) or non-monotonically affect on \(R_0\) , depending on the choice of spatial transition rate from altered to normal behaviors. Our results reveal the importance of behavior changes on threshold level, and non-monotonic variation patterns in \(R_0\) are induced by the spatial transitions between groups with different behaviors.
