This paper is concerned with analysis of the global behavior for a type of reaction-diffusion system incorporating the pathogens' incubation period, which describes the infection of bacteria in a population. By using the operator semigroup theory and dynamical system approaches, the global dynamics with respect to the homogeneous Dirichlet problem are investigated. Firstly, the positivity, boundedness, compactness, and smoothness of the semiflow are obtained. Then, we study the topology on the omega-limit set and the dynamical behaviors, including permanence, existence, uniqueness and attracti...
