Stage-Structured ImpulsiveSIModel for Pest Management release_t7ucztdfwzd6he5calylyvs3t4

Abstract

An<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E2"><mml:mrow><mml:mi>S</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:math>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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="E3"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mover accent="true"><mml:mi>I</mml:mi><mml:mo stretchy="true">˜</mml:mo></mml:mover><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>, and a condition for the permanence of the system. At last, a brief discussion shows that our results will be helpful for pest management.
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