Global behavior of a reaction-diffusion model with time delay and Dirichlet condition

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 attractiveness of nontrivial steady-state solutions. Finally, our main results are employed to characterize threshold dynamics for two special models with Rick type and Mackey-Glass type infectivity nonlinearities respectively. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper explores the global behavior of a reaction-diffusion system describing bacterial infection in a population, considering the pathogens' incubation period. The study uses operator semigroup theory and dynamical system approaches to investigate the global dynamics with respect to the homogeneous Dirichlet problem. The analysis includes the positivity, boundedness, topology, permanence, and threshold dynamics for special models with different infectivity nonlinearities.