Analysis of an SIS reaction-diffusion-chemotaxis epidemic model with gradient-dependent flux limitation and standard incidence

In this paper, we are dedicated to an SIS reaction-diffusion-chemotaxis epidemic model with cross-diffusion including gradient-dependent flux limitation and standard incidence in spatially heterogeneous environments. We first establish the existence of the globally bounded classical solution to the corresponding Neumann initial-boundary value problem for arbitrary reasonably regular initial data. Moreover, for initial data of small size, a result concerning global classical solvability is obtained provided that the space-dependent recruitment rate of susceptibles is suitably small.