The dynamics of an impulsive predator–prey model with communicable disease in the prey species only

We investigate an impulsive predator prey model with communicable disease.Susceptible pests will perish if impulsive period is smaller than a critical value.The smaller impulsive period is, the faster the susceptible pests go to extinction.Numerical simulations validate the obtained theoretical results. In this paper, we propose an impulsive predator-prey model with communicable disease in the prey species only and investigate its interesting biological dynamics. By the Floquet theory of impulsive differential equation and small amplitude perturbation skills, we have deduced the sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the proposed model. We also give the existences of the "infection-free" periodic solution and the "predator-free" solution. Finally, numerical results validate the effectiveness of theoretical analysis for the proposed model in this paper.