Pest regulation by means of impulsive controls

In this paper, we consider an integrated pest management model which is impulsively controlled by means of biological and chemical controls. These controls are assumed to act in a periodic fashion, a nonlinear incidence rate being used to account for the dynamics of the disease caused by the application of the biological control. The Floquet theory for impulsive ordinary differential equations is employed to obtain a condition in terms of an inequality involving the total action of the nonlinear force of infection in a period, under which the susceptible pest-eradication solution is globally asymptotically stable. If the opposite inequality is satisfied, then it is shown that the system under consideration becomes uniformly persistent. A biological interpretation of the persistence condition is also provided.