Dynamics of a generalized predator-prey model with delay and impulse via the basic reproduction number

摘要

In this paper, we study a generalized predator-prey model with delay and impulse. The existence of the predator-free periodic solution is investigated. We employ the approach and techniques coming from epidemiology and calculate the basic reproduction number for the predator. Using the basic reproduction number, we consider the global attraction of the predator-free periodic solution and permanence of the model. As for application, an example is discussed. Furthermore, some numerical simulations are given to illustrate our results.