Dynamic Analysis of a SI System with Periodic Biological and Chemical Control

In this paper, we consider a SI system with spraying microbial pesticide and releasing the infected pests, the infected pests have the function similar to the microbial pesticide and can infect the healthy pests, further weaken or disable their prey function till death. By applying the Floquet theorem of linear periodic impulsive equations and the comparison theorem, we show that there exists a globally asymptotically stable pest eradication periodic solution when the impulsive period is less than the critical value τmax, we further prove that the system is uniformly permanent if the impulsive period τ > τmax. Thus, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels. Mathematics Subject Classification: 34C05, 92D25