Dynamic analysis of pest control model with population dispersal in two patches and impulsive effect

In this paper, we investigate the pest control model with population dispersal in two patches and impulsive effect. By exploiting the Floquet theory of impulsive differential equation and small amplitude perturbation skills, we can obtain that the susceptible pest eradication periodic solution is globally asymptotically stable if the impulsive periodic tau is less than the critical value tau(0). Further, we also prove that the system is permanent when the impulsive periodic tau is larger than the critical value tau(0). Hence, in order to drive the susceptible pest to extinction, we can take impulsive control strategy such that tau<tau(0) according to the effect of the viruses on the environment and the cost of the releasing pest infected in a laboratory. Finally, numerical simulations validate the obtained theoretical results for the pest control model with population dispersal in two patches and impulsive effect. (C) 2014 Elsevier B.V. All rights reserved.