Asymptotic profiles of basic reproduction number for a degenerate reaction–diffusion host–pathogen model

In this paper, the basic reproduction number (BRN) is explored in terms of a degenerate reaction–diffusion host–pathogen model. The expressions of BRN and local basic reproduction number (LBRN) for the model are calculated. Some basic properties of with respect to the general diffusion rates and the asymptotic profiles of with respect to large diffusion rates and small diffusion rates are established by introducing two compact operators and . Our results reveal that is the spectral radius of a sum of the product of additive operators and strongly positive compact linear operators with spectral radii one.