A impulsive infective transmission SI model for pest control

In this paper, we propose a model with impulsive control of epidemics for pest management. By using Floquetʹs theorem, smallamplitude perturbation skills and comparison theorem, we show that there exists a globally asymptotically stable susceptible pesteradication periodic solution when the release amount of infective pests is larger than some critical value. However, when the amount of infective pests released is less than this critical value, the system is shown to be permanent, which implies that the trivial periodic susceptible pest-eradication solution loses its stability. Further, the existence of a positive periodic endemic solution and other rich dynamics are also studied by numerical simulation. Therefore, we can use the amount of release of infective pests to control susceptible pests at desirable low levels.