Endemic dynamics in a host–parasite epidemiological model within spatially heterogeneous environment

In this paper, we investigate the endemic dynamics in a host–parasite model under combined frequency- and density-dependent transmission in a spatially heterogeneous environment. We give some properties of the parasite-free and parasite-driven extinction stationary solutions, and prove that the positive stationary solution set forms a bounded continuum which connects the parasite-free and parasite-driven extinction stationary solutions sets.