skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Stability and permanence of an eco-epidemiological SEIN model with impulsive biological control

Abstract

Natural enemies of insects are extremely important in preventing pest outbreaks in crop fields. Therefore, we investigate the dynamical behavior of a pest-dependent consumption pest–natural enemy (i.e., prey–predator) SEIN model concerning diseases in pest population with three classes (susceptible–exposed–infectious) and impulsive releasing of infectious pests and natural enemies at fixed moments of time. We prove that all solutions of the system are uniformly ultimately bounded. In first part of the main results, the sufficient conditions for local as well as global asymptotic stability of the susceptible and exposed pest extinction periodic solution are determined using a Floquet’s theorem of impulsive differential equations, small-amplitude perturbation skills and comparison theorem. In second part, the sufficient condition for the permanence of a system is determined. These dynamics imply that susceptible and exposed pest populations become extinct when impulse period is less than some critical value and pests coexist with natural enemies at low level when impulse period crosses the critical value. Thus, our results provide some reliable theoretical tactics for pest management and finally these are verified by performing some numerical simulations.

Authors:
 [1];  [2]
  1. Dr. Harisingh Gour Vishwavidyalaya, Department of Mathematics and Statistics (India)
  2. ABV-Indian Institute of Information Technology and Management, Department of Applied Sciences (India)
Publication Date:
OSTI Identifier:
22769370
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CHAOS THEORY; COMPUTERIZED SIMULATION; CONTROL; CROPS; DIFFERENTIAL EQUATIONS; DISEASES; INSECTS

Citation Formats

Mathur, Kunwer Singh, E-mail: sing1709@gmail.com, and Dhar, Joydip. Stability and permanence of an eco-epidemiological SEIN model with impulsive biological control. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0365-1.
Mathur, Kunwer Singh, E-mail: sing1709@gmail.com, & Dhar, Joydip. Stability and permanence of an eco-epidemiological SEIN model with impulsive biological control. United States. doi:10.1007/S40314-016-0365-1.
Mathur, Kunwer Singh, E-mail: sing1709@gmail.com, and Dhar, Joydip. Thu . "Stability and permanence of an eco-epidemiological SEIN model with impulsive biological control". United States. doi:10.1007/S40314-016-0365-1.
@article{osti_22769370,
title = {Stability and permanence of an eco-epidemiological SEIN model with impulsive biological control},
author = {Mathur, Kunwer Singh, E-mail: sing1709@gmail.com and Dhar, Joydip},
abstractNote = {Natural enemies of insects are extremely important in preventing pest outbreaks in crop fields. Therefore, we investigate the dynamical behavior of a pest-dependent consumption pest–natural enemy (i.e., prey–predator) SEIN model concerning diseases in pest population with three classes (susceptible–exposed–infectious) and impulsive releasing of infectious pests and natural enemies at fixed moments of time. We prove that all solutions of the system are uniformly ultimately bounded. In first part of the main results, the sufficient conditions for local as well as global asymptotic stability of the susceptible and exposed pest extinction periodic solution are determined using a Floquet’s theorem of impulsive differential equations, small-amplitude perturbation skills and comparison theorem. In second part, the sufficient condition for the permanence of a system is determined. These dynamics imply that susceptible and exposed pest populations become extinct when impulse period is less than some critical value and pests coexist with natural enemies at low level when impulse period crosses the critical value. Thus, our results provide some reliable theoretical tactics for pest management and finally these are verified by performing some numerical simulations.},
doi = {10.1007/S40314-016-0365-1},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 1,
volume = 37,
place = {United States},
year = {2018},
month = {3}
}