Mathematical models for the control of a pest population by infected pest

In this paper, we propose two mathematical models concerning continuous and impulsive pest control strategies, respectively. Therefore, our models are the ordinary differential equations and the impulsive differential equations. As a result, the global asymptotic stability of the equilibria of the ordinary differential equations is studied. In the case when an impulsive control is used, it is observed that there exists a globally asymptotically stable susceptible pest-eradication periodic solution when the amount of infective pests released periodically is larger than some critical value. 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 susceptible pest-eradication solution loses its stability. Finally, by means of numerical simulation, we obtain the critical values of the control variable under different methods of release of infected pests.