Role of transmissible disease in an infected prey-dependent predator-prey system

Mainul Haque; Joydev Chattopadhyay

doi:10.1080/13873950600682580

Role of transmissible disease in an infected prey-dependent predator-prey system

Mainul Haque^*
, Joydev Chattopadhyay

^*Corresponding author for this work

Research output: Journal Publication › Article › peer-review

23 Citations (Scopus)

Abstract

The role of disease in ecological systems is a very important issue from both mathematical and ecological points of view. This paper deals with the qualitative analysis of a prey-dependent predator-prey system in which a disease is spreading among the prey species only. We have analysed the behaviour of the system around each equilibrium and obtained conditions for global stability of the system around an equilibrium by using suitable Lypunov functions. We have also worked out the region of parametric space under which the system enters a Hopf bifurcation and a transcritical bifurcation but does not experience either saddle-node bifurcations or pitchfork bifurcations around the disease-free equilibrium E2. Finally, we have given an example of a real ecological situation with experimental data simulations.

Original language	English
Pages (from-to)	163-178
Number of pages	16
Journal	Mathematical and Computer Modelling of Dynamical Systems
Volume	13
Issue number	2
DOIs	https://doi.org/10.1080/13873950600682580
Publication status	Published - Apr 2007
Externally published	Yes

UN SDGs

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

SDG 3 Good Health and Well-being
SDG 15 Life on Land

Free Keywords

Eco-epidemiology
Global stability
Hopf bifurcation
Local stability
Pitchfork bifurcation
Saddle-node bifurcation
Transcritical bifurcation

ASJC Scopus subject areas

Control and Systems Engineering
Software
Modelling and Simulation
Computer Science Applications
Applied Mathematics

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10.1080/13873950600682580

Cite this

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title = "Role of transmissible disease in an infected prey-dependent predator-prey system",

abstract = "The role of disease in ecological systems is a very important issue from both mathematical and ecological points of view. This paper deals with the qualitative analysis of a prey-dependent predator-prey system in which a disease is spreading among the prey species only. We have analysed the behaviour of the system around each equilibrium and obtained conditions for global stability of the system around an equilibrium by using suitable Lypunov functions. We have also worked out the region of parametric space under which the system enters a Hopf bifurcation and a transcritical bifurcation but does not experience either saddle-node bifurcations or pitchfork bifurcations around the disease-free equilibrium E2. Finally, we have given an example of a real ecological situation with experimental data simulations.",

keywords = "Eco-epidemiology, Global stability, Hopf bifurcation, Local stability, Pitchfork bifurcation, Saddle-node bifurcation, Transcritical bifurcation",

author = "Mainul Haque and Joydev Chattopadhyay",

note = "Funding Information: Part of this work was done when the first author, M. Haque, visited North University of China, P.R. China, under the financial support of the National Natural Science Foundation of China (10471040). The authors are thankful to Professor Zhen Jin, North University of China, Taiyuan, Shanxi, P.R. China, for his careful reading of the earlier version of this manuscript. The authors are also grateful to the referees for their constructive criticisms and valuable suggestions which were necessary to improve the quality of this article.",

year = "2007",

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doi = "10.1080/13873950600682580",

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volume = "13",

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T1 - Role of transmissible disease in an infected prey-dependent predator-prey system

AU - Haque, Mainul

AU - Chattopadhyay, Joydev

N1 - Funding Information: Part of this work was done when the first author, M. Haque, visited North University of China, P.R. China, under the financial support of the National Natural Science Foundation of China (10471040). The authors are thankful to Professor Zhen Jin, North University of China, Taiyuan, Shanxi, P.R. China, for his careful reading of the earlier version of this manuscript. The authors are also grateful to the referees for their constructive criticisms and valuable suggestions which were necessary to improve the quality of this article.

PY - 2007/4

Y1 - 2007/4

N2 - The role of disease in ecological systems is a very important issue from both mathematical and ecological points of view. This paper deals with the qualitative analysis of a prey-dependent predator-prey system in which a disease is spreading among the prey species only. We have analysed the behaviour of the system around each equilibrium and obtained conditions for global stability of the system around an equilibrium by using suitable Lypunov functions. We have also worked out the region of parametric space under which the system enters a Hopf bifurcation and a transcritical bifurcation but does not experience either saddle-node bifurcations or pitchfork bifurcations around the disease-free equilibrium E2. Finally, we have given an example of a real ecological situation with experimental data simulations.

AB - The role of disease in ecological systems is a very important issue from both mathematical and ecological points of view. This paper deals with the qualitative analysis of a prey-dependent predator-prey system in which a disease is spreading among the prey species only. We have analysed the behaviour of the system around each equilibrium and obtained conditions for global stability of the system around an equilibrium by using suitable Lypunov functions. We have also worked out the region of parametric space under which the system enters a Hopf bifurcation and a transcritical bifurcation but does not experience either saddle-node bifurcations or pitchfork bifurcations around the disease-free equilibrium E2. Finally, we have given an example of a real ecological situation with experimental data simulations.

KW - Eco-epidemiology

KW - Global stability

KW - Hopf bifurcation

KW - Local stability

KW - Pitchfork bifurcation

KW - Saddle-node bifurcation

KW - Transcritical bifurcation

UR - https://www.scopus.com/pages/publications/33947361660

U2 - 10.1080/13873950600682580

DO - 10.1080/13873950600682580

M3 - Article

AN - SCOPUS:33947361660

SN - 1387-3954

VL - 13

SP - 163

EP - 178

JO - Mathematical and Computer Modelling of Dynamical Systems

JF - Mathematical and Computer Modelling of Dynamical Systems

IS - 2

ER -

Role of transmissible disease in an infected prey-dependent predator-prey system

Abstract

UN SDGs

Free Keywords

ASJC Scopus subject areas

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