Title: Stability analysis of an eco-epidemiological SIN model with impulsive control strategy for integrated pest management considering stage-structure in predator
Authors: Preety Kalra; Maninderjit Kaur
Addresses: Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara 144001, India ' Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara 144001, India
Abstract: Pest outbreak is a major threat to agricultural resources and livestock. Integrated pest management is widely being used nowadays to control the pest population. Natural enemies are immensely beneficial to control the outbreak of pests. To achieve the same, in this paper, microbial and biological pest control techniques are applied simultaneously by impulsively releasing natural enemies and infected pests. Therefore a SIN (prey-predator) model considering infection in prey with two classes (susceptible-infected) and stage structure in predator is investigated for the cause of integrated pest management. Prey acts as pest and predator plays the role of a natural enemy. Firstly, local and global stability of pest extinction periodic solution is carried out, then condition for the permanence of system is derived using Stroboscopic map, comparison analysis technique and Floquet theory of impulsive differential equations. Further, it is observed that there exists a threshold value of the impulsive period which plays an important role in the dynamics of the system. Finally, for validating the established results, numerical simulation is done using MATLAB.
Keywords: biological control; impulsive control strategy; pest management; stage-structure.
International Journal of Mathematical Modelling and Numerical Optimisation, 2022 Vol.12 No.1, pp.43 - 68
Received: 23 Jul 2020
Accepted: 03 Mar 2021
Published online: 20 Dec 2021 *