Spatial heterogeneity in behavioral responses and human mobility can jointly shape epidemic dynamics, yet their interaction has received limited attention due to analytical challenges. Here we develop a reaction-diffusion model coupling imitation-based behavioral switching with disease transmission, where the switching process is driven by differences in strategy payoffs. We define the basic reproduction number and characterize the threshold dynamics of the system. A key analytical step is to establish the ultimate boundedness of solutions in the presence of nonlinear behavioral switching terms. Furthermore, we analyze the asymptotic profiles of endemic equilibria under three limiting diffusion regimes. Our numerical results show that the effect of behavioral switching on long-term prevalence is threshold dependent and that spatial heterogeneity in behavior change can reduce disease prevalence under appropriate parameter regimes. Interestingly, increasing the mean switching rate enhances the protective effect of behavioral switching, whereas increasing the mean perceived threshold weakens this effect and may even reverse it for sufficiently large infected diffusion. In addition, the interaction between human mobility and behavioral heterogeneity can lead to non-monotone pattern in disease prevalence.
We focus on the long-term dynamics of an impulsive nonlocal dispersal system with nonlocal pulses on time-varying domains, including the asymptotically fixed, asymptotically time-periodic, and asymptotically unbounded cases. We first establish the well-posedness of the impulsive system and reduce its dynamics to a nonautonomous discrete-time process. For the asymptotically bounded cases, we characterize the threshold dynamics of the original impulsive system by combining the spectral properties and global dynamics of the limiting system with the theory of internally chain transitive sets. The asymptotically unbounded case presents an additional difficulty due to the interplay between time-dependent nonlocal dispersal and nonlocal impulsive effects, for which the limiting dynamics alone are insufficient to derive the required estimates. To overcome this difficulty, we develop an incremental subsolution method, in which a parametrized family of subsolutions is advanced through successive positive increments. Using this construction, we establish the global dynamics of positive solutions.