Dynamics of a generalized nonlocal dispersion SIS epidemic model

This paper explores a generalized nonlocal dispersion SIS epidemic model subject to the Neumann boundary conditions and spatial heterogeneity. We use a convolution operator to describe the nonlocal spatial movements of individuals. Our primary goal is to investigate this model, focusing on a generalized incidence function, which presents an additional challenge in the model analysis. This model’s basic reproduction number, R₀, is identified, and it is proved that 1-R₀ has the same sign as the principal eigenvalue of a generalized linear nonlocal operator. Furthermore, the asymptotic profiles of R₀ in terms of dispersion coefficients are also established. We also investigate the existence and uniqueness of an endemic steady state for R₀>1, and we study the large dispersal rates effect on the asymptotic profiles of the steady endemic state. Finally, we discussed the global asymptotic behavior of the solution for different dispersal coefficients.