## 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 $$(0,0,\tilde I(t))$$, 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:

 37N25 Dynamical systems in biology 92D30 Epidemiology 34K45 Functional-differential equations with impulses 34K20 Stability theory of functional-differential equations
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### References:

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