Dynamics of pest population: Effect of diseased pest and pesticide

Abstract

This paper is mainly concerned with an investigation of a non-linear plant pest model with stage structured pest population and introduction of impulsive infected pest population and chemical pesticides as the control parameters. Several mathematical models have been introduced in the literature to gain insight of plant-pest natural enemy model, however, the results considering the effect of infected pest population as well as pesticides are not involved. Further, stability analysis of pest extinction equilibrium on the basis of level of infected pest as well as impulsive period is also a new advancement in this paper which has not been discussed earlier. Hence, the paper introduces a four-dimensional mathematical model through impulsive differential equation. The overall contribution of the paper includes construction of a non-linear mathematical model, positivity and boundedness of the system, global stability of the pest extinction equilibrium point based on thresholds, permanence of the system. Finally, the numerical simulation is performed to validate the effectiveness and applicability of the theoretical predictions.