Global dynamics of a delayed two-patch discrete SIR disease model

Abstract

In this paper, we propose a delayed discrete SIR disease model with a saturate incidence rate and extend it to a patchy environment by taking the dispersal of susceptible individuals from one patch to the other into consideration. For the single-patch model, we establish the global threshold dynamics by the method of Lyapunov functionals. For the two-patch model, we show that the global dynamics of the disease-free equilibrium, two boundary endemic equilibria and the interior endemic equilibrium are determined by several threshold quantities. We also explore the impacts of the dispersal on the disease dynamics. Our interesting findings may provide some useful insights on how to properly manage the dispersal between different regions to control the spread of diseases.