On cognitive epidemic models: spatial segregation versus nonpharmaceutical interventions

Fick's law and the Fokker-Planck law of diffusion are applied to manifest the cognitive dispersal of individuals in two reaction-diffusion SEIR epidemic models, where the disease transmission is illustrated by nonlocal infection mechanisms in heterogeneous environments. Building upon the well-posedness of solutions, threshold dynamics are discussed in terms of the basic reproduction numbers for the two cognitive epidemic models. The numerical investigation reveals that the Fokker-Planck law can better describe the diffusion of individuals by taking different dispersal strategies of exposed individuals in our cognitive epidemic models, and provides some insights on spatial segregation and nonpharmaceutical interventions: (i) spatial segregation occurs in the random diffusion model when the nonlocal infection radius is small, while it appears in the symmetric diffusion model when the radius is large; (ii) nonpharmaceutical interventions on restricting the dispersal of exposed and infected individuals do not contribute to reducing the infection proportion, but rather eliminate the disease in a region, which expands as the nonlocal infection radius increases. We additionally find that the final infection size in the random diffusion model is significantly smaller than that in the symmetric diffusion model and decreases as the nonlocal infection radius increases.