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Stage-structured impulsive SI model for pest management. (English) Zbl 1146.37368
Summary: An SI epidemic model with stage structure is investigated. In the model, impulsive biological control is taken, that is, we release infected pests to the field at a fixed time periodically. We get a sufficient condition for the global asymptotical stability of the pest-eradication periodic solution (0,0,I ˜(t)), and a condition for the permanence of the system. At last, a brief discussion shows that our results will be helpful for pest management.
MSC:
37N25Dynamical systems in biology
92D30Epidemiology
34K45Functional-differential equations with impulses
34K20Stability theory of functional-differential equations