Mathematical modelling to control a pest population by infected pests. (English) Zbl 1205.34065

Summary: In this paper, we formulate and investigate the pest control models in accordance with the mathematical theory of epidemiology. We assume that the release of infected pests is continuous and impulsive, respectively. Therefore, our models are the ordinary differential equations and the impulsive differential equations. We study the global stability of the equilibria of the ordinary differential equations. The permanence of the impulsive differential equations is proved. By means of numerical simulation, we obtain the critical values of the control variable under different methods of release of infected pests. Thus, we provide a mathematical evidence in the management of an epidemic controlling a pest.


34D20 Stability of solutions to ordinary differential equations
92D25 Population dynamics (general)
92D30 Epidemiology
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