Role of Bio-Pest Control on Theta Logistic Populations: A Case Study on Jatropha Curcus Cultivation System

Abstract

Renewable crops are the most demanding source for biodiesel production. Jatropha sp. oil has shown promising features in generating renewable energy source. Presently, the crop cultivation faces severe damage to the seed production during pest invasion. We consider a nonlinear mathematical system with biomass of Jatropha sp., susceptible pest population, infected pest population and virus population. The biomass of Jatropha sp. and susceptible pest population follows theta logistic growth as theta logistic growth curve is a more natural choice in comparison with the classical logistic growth curve model. Introduction of pest control by the application of Nuclear Polyhedrosis Virus (NPV) was applied through foliar spraying to arrest the pest invasion. The values of θ have to depend on the process of interaction at different densities. In this research communication we observe how various values of theta can affect crop survival during pest invasion which makes the model biologically more realistic. Stability and bifurcation analyses have been worked out for the system. Analytically and numerically we find out the threshold value of θ = 0.74. We have seen that for θ < 0.74 the system is stable and for θ ≥ 0.74, the system shows limit cycle oscillation which holds upto θ = 1. Analytical and numerical results based on simulated findings validate our mathematical model.