An impulsively controlled predator–pest model with disease in the pest

In this paper, we consider an integrated pest management model with disease in the pest and a stage structure for its natural predator, which is subject to impulsive and periodic controls. A nonlinear incidence rate expressed in an abstract form, is used to describe the propagation of the disease, which is spread through the periodic release of infective pests, the functional response of the mature predator also being given in an abstract, unspecified form. Sufficient conditions for the local and global stability of the susceptible pest-eradication periodic solution are found by means of Floquet theory and comparison methods, the permanence of the system also being discussed. These stability conditions are shown to be biologically significant, being reformulated as balance conditions for the susceptible pest class.