Stability and permanence of an eco-epidemiological SEIN model with impulsive biological control

Abstract

Natural enemies of insects are extremely important in preventing pest outbreaks in crop fields. Therefore, we investigate the dynamical behavior of a pest-dependent consumption pest–natural enemy (i.e., prey–predator) SEIN model concerning diseases in pest population with three classes (susceptible–exposed–infectious) and impulsive releasing of infectious pests and natural enemies at fixed moments of time. We prove that all solutions of the system are uniformly ultimately bounded. In first part of the main results, the sufficient conditions for local as well as global asymptotic stability of the susceptible and exposed pest extinction periodic solution are determined using a Floquet’s theorem of impulsive differential equations, small-amplitude perturbation skills and comparison theorem. In second part, the sufficient condition for the permanence of a system is determined. These dynamics imply that susceptible and exposed pest populations become extinct when impulse period is less than some critical value and pests coexist with natural enemies at low level when impulse period crosses the critical value. Thus, our results provide some reliable theoretical tactics for pest management and finally these are verified by performing some numerical simulations.