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A predator-prey model with disease in the prey and two impulses for integrated pest management. (English) Zbl 1185.34015
Summary: In this paper, a predator-prey model with disease in the prey is constructed and investigated for the purpose of integrated pest management. In the first part of the main results, the sufficient condition for the global stability of the susceptible pest-eradication periodic solution is obtained, which means if the release amount of infective prey and predator satisfy the condition, then the pest will be controlled. The sufficient condition for the permanence of the system is also obtained subsequently, which means if the release amount of infective prey and predator satisfy the condition, then the prey and the predator will coexist. At last, we interpret our mathematical results.
MSC:
34A37Differential equations with impulses
92D25Population dynamics (general)
34C11Qualitative theory of solutions of ODE: growth, boundedness
34C25Periodic solutions of ODE
92D30Epidemiology
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