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A stage structured predator-prey model with infectious disease in the prey. (Chinese. English summary) Zbl 1190.92045

Summary: A stage structured impulsive delayed predator-prey model with infectious disease in the prey is considered. Sufficient conditions for the global attractivity of susceptible pest-eradication periodic solutions are obtained by using corresponding theories and methods of impulsive delayed differential equations. Furthermore, it is obtained that the susceptible pest population can be controlled under the economic injury level (EIL) if the impulsive period is within an appropriate range, that is, the susceptible pest population and the natural enemy population may coexist. Our results provide a reliable basis for practical pest management.

MSC:

92D40 Ecology
92D30 Epidemiology
34K45 Functional-differential equations with impulses
34K35 Control problems for functional-differential equations
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