Stability Analysis of Integrated Pest Management with Impulsive Biological Control

Bhanu Gupta Bhanu Gupta,Sanjay K Srivastava Sanjay K Srivastava,Amit Sharma Amit Sharma

doi:10.15415/mjis.2018.62007

Abstract

The aim of the present work is to study the dynamics of stage-structured pest control model including biological control, i.e. by releasing of natural enemies and infected pests periodically. It is assumed that only immature susceptible pests are attacked by natural enemies admitting Beddington DeAngelis functional response and mature susceptible pests are contacted by infected pests with bilinear incidence rate and become exposed. The sufficient condition for local stability of pest extinction periodic solution is derived by making use of Floquet’s theory and small amplitude perturbation technique. The global attractivity of pest extinction periodic solution is also established by applying comparison principle of impulsive differential equations.

Highlights

Farmers have a vast scope of pest control methods categorized into physical control, biological control, chemical control and wireless sensing
It is assumed that only immature susceptible pests are attacked by natural enemies admitting Beddington DeAngelis functional response and mature susceptible pests are contacted by infected pests with bilinear incidence rate and become exposed
The global attractivity of pest extinction periodic solution is established by applying comparison principle of impulsive differential equations

Summary

INTRODUCTION

Farmers have a vast scope of pest control methods categorized into physical control, biological control, chemical control and wireless sensing. B Sharma, A Srivastava, SK releasing the natural enemies of pests and /or by spreading infection among the pest population. Xiang et al (2009) and Wang and Song (2010) worked on susceptible-exposed-infected (SEI) pest management models. Susceptible-exposed-infected-natural enemy (SEIN) models are more important as they give more significant results from biological view point. ∆N1(t) = p2, where S1(t), E1(t), I1(t) and N1(t) represents the densities of susceptible pests, exposed pests, infected pests and natural enemies respectively. Negi and Gakkhar (2007) studied the dynamics of Beddington-DeAngelis prey-predator mathematical model with impulsive harvesting. Cantrell and Cosner (2001) and Wang and Huang (2015) discussed the prey-predator model using Beddington-DeAngelis type interactions.

MATHEMATICAL MODEL

PRELIMINARIES

STABILITY ANALYSIS