IMPULSIVE CONTROL OF A TWO-PATCH INTEGRATED PEST MANAGEMENT MODEL

We hereby consider a two-patch SI integrated pest management model with dispersal of susceptible pests between patches, which is subject to periodic impulsive biological and chemical controls. The biological control consists in the periodic release of infective pests, in a constant amount, while the chemical control consists in periodic pesticide spraying, which causes the removal of fixed proportions of the infective and susceptible pest populations, respectively. The spread of the disease inflicted by the release of infective pests is characterized by a nonlinear incidence rate of infection expressed in an abstract, unspecified form. A sufficient condition for the local stability of the susceptible pest-eradication periodic solution is obtained through the use of Floquet theory for impulsive and periodic ordinary differential equations, the effect of population dispersal between patches upon the stability of this solution being then investigated for several particular cases. 2000 Mathematics Subject Classification: 92D40, 34A37.

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