Abstract
We investigate a periodic predator-prey system subject to impulsive perturbations, in which a disease can be transmitted among the prey species only, in this paper. With the help of the theory of impulsive differential equations and Lyapunov functional method, sufficient conditions for the permanence, global attractivity, and partial extinction of system are established, respectively. It is shown that impulsive perturbations contribute to the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.
Highlights
As a relatively new branch of study in theoretical biology, ecoepidemiology can be viewed as the coupling of ecology and epidemiology
A natural description of the motion of impulsive processes can be expressed by impulsive differential equations
It follows from the comparison theorem of impulsive differential equations that min t∈[0,ω]
Summary
As a relatively new branch of study in theoretical biology, ecoepidemiology can be viewed as the coupling of ecology and epidemiology. In reality, many evolution processes are characterized by the fact that they experience changes of state suddenly These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Some impulsive equations have been introduced in ecoepidemiological models in relation to chemotherapeutic [7] and vaccination [8, 9] and population disease control [10, 11]. Considering the above facts, in this paper, we will consider a periodic predator-prey model subject to impulsive perturbations, in which a disease can be transmitted among the prey species only. Our motive comes from a delayed nonautonomous predator-prey system with disease in the prey in [5], and we consider the effect of impulsive perturbations on a corresponding undelayed periodic version in this paper. By Lyapunov functional method, we will establish sufficient conditions for the global attractivity of the system
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