Modeling of Insect-Pathogen Dynamics with Biological Control

Abstract

In this work, a model has been proposed to analyze the effect of wild plant species on biologically-based technologies for pest control. It is assumed that the pest species have a second food source (wild host plants) except crops. Analytical results prove that the model is well-posed as the system variables are positive and uniformly bounded. The permanence of the system has been verified. Equilibrium points and corresponding stability analysis have also been performed. Numerical figures have supported the fact that the interior steady state if it exists, remains stable for any transmission rate. Henceforth biological control has a stabilizing effect. Furthermore, the results prove that biological control is beneficial not only for wild plants but for crops too.