An impulsive predator-prey model with communicable disease in the prey species only

Maoxing Liu; Zhen Jin; Mainul Haque

doi:10.1016/j.nonrwa.2008.10.010

An impulsive predator-prey model with communicable disease in the prey species only

Maoxing Liu, Zhen Jin, Mainul Haque

School of Mathematical Sciences

Research output: Journal Publication › Article › peer-review

24 Citations (Scopus)

Abstract

A system of impulsive differential equations describing predator-prey dynamics with impulsive effect is proposed and analyzed with the assumption that a transmissible disease is spreading among the prey species only. At first, the "semi-trivial" periodic solution (S (t), 0, 0) is given. After that, the existence of "infection-free" periodic solution (S (t), 0, P (t)) and the "predator-free" periodic solution have been obtained via bifurcation. Finally, the method of coincidence degree has been used to derive a set of sufficient conditions for the existence of at least one strictly positive periodic solution. Numerical simulations and a brief discussion conclude the paper.

Original language	English
Pages (from-to)	3098-3111
Number of pages	14
Journal	Nonlinear Analysis: Real World Applications
Volume	10
Issue number	5
DOIs	https://doi.org/10.1016/j.nonrwa.2008.10.010
Publication status	Published - Oct 2009

Keywords

Bifurcation
Coincidence degree
Eco-epidemiology
Impulsive effect
Infected prey
Predator
Susceptible prey

ASJC Scopus subject areas

General Engineering
Computational Mathematics
Analysis
Applied Mathematics
General Economics,Econometrics and Finance

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/j.nonrwa.2008.10.010

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Liu, M., Jin, Z., & Haque, M. (2009). An impulsive predator-prey model with communicable disease in the prey species only. Nonlinear Analysis: Real World Applications, 10(5), 3098-3111. https://doi.org/10.1016/j.nonrwa.2008.10.010

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title = "An impulsive predator-prey model with communicable disease in the prey species only",

abstract = "A system of impulsive differential equations describing predator-prey dynamics with impulsive effect is proposed and analyzed with the assumption that a transmissible disease is spreading among the prey species only. At first, the {"}semi-trivial{"} periodic solution (S (t), 0, 0) is given. After that, the existence of {"}infection-free{"} periodic solution (S (t), 0, P (t)) and the {"}predator-free{"} periodic solution have been obtained via bifurcation. Finally, the method of coincidence degree has been used to derive a set of sufficient conditions for the existence of at least one strictly positive periodic solution. Numerical simulations and a brief discussion conclude the paper.",

keywords = "Bifurcation, Coincidence degree, Eco-epidemiology, Impulsive effect, Infected prey, Predator, Susceptible prey",

author = "Maoxing Liu and Zhen Jin and Mainul Haque",

note = "Funding Information: A crucial part of this work was done when the third author Mainul Haque visited the North University of China, PR China, with the financial support of National Natural Science Foundation of China (10471040).",

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doi = "10.1016/j.nonrwa.2008.10.010",

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AU - Liu, Maoxing

AU - Jin, Zhen

AU - Haque, Mainul

N1 - Funding Information: A crucial part of this work was done when the third author Mainul Haque visited the North University of China, PR China, with the financial support of National Natural Science Foundation of China (10471040).

PY - 2009/10

Y1 - 2009/10

N2 - A system of impulsive differential equations describing predator-prey dynamics with impulsive effect is proposed and analyzed with the assumption that a transmissible disease is spreading among the prey species only. At first, the "semi-trivial" periodic solution (S (t), 0, 0) is given. After that, the existence of "infection-free" periodic solution (S (t), 0, P (t)) and the "predator-free" periodic solution have been obtained via bifurcation. Finally, the method of coincidence degree has been used to derive a set of sufficient conditions for the existence of at least one strictly positive periodic solution. Numerical simulations and a brief discussion conclude the paper.

AB - A system of impulsive differential equations describing predator-prey dynamics with impulsive effect is proposed and analyzed with the assumption that a transmissible disease is spreading among the prey species only. At first, the "semi-trivial" periodic solution (S (t), 0, 0) is given. After that, the existence of "infection-free" periodic solution (S (t), 0, P (t)) and the "predator-free" periodic solution have been obtained via bifurcation. Finally, the method of coincidence degree has been used to derive a set of sufficient conditions for the existence of at least one strictly positive periodic solution. Numerical simulations and a brief discussion conclude the paper.

KW - Bifurcation

KW - Coincidence degree

KW - Eco-epidemiology

KW - Impulsive effect

KW - Infected prey

KW - Predator

KW - Susceptible prey

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DO - 10.1016/j.nonrwa.2008.10.010

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AN - SCOPUS:64049112970

SN - 1468-1218

VL - 10

SP - 3098

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JO - Nonlinear Analysis: Real World Applications

JF - Nonlinear Analysis: Real World Applications

IS - 5

ER -

An impulsive predator-prey model with communicable disease in the prey species only

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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