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Volume 26, Issue 1
Analysis of a Prey-Predator Model with Disease in Prey

Jianjun Li, Wenjie Gao & Peng Sun

Commun. Math. Res., 26 (2010), pp. 27-40.

Published online: 2021-05

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  • Abstract

In this paper, a system of reaction-diffusion equations arising in eco-epidemiological systems is investigated. The equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases. Local stability of the constant positive solution is considered. A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given. It is proved that if the diffusion coefficient of the prey with disease is treated as a bifurcation parameter, non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.

  • Keywords

eco-epidemiology, bifurcation, non-constant positive steady solution.

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COPYRIGHT: © Global Science Press

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@Article{CMR-26-27, author = {Li , JianjunGao , Wenjie and Sun , Peng}, title = {Analysis of a Prey-Predator Model with Disease in Prey}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {26}, number = {1}, pages = {27--40}, abstract = {

In this paper, a system of reaction-diffusion equations arising in eco-epidemiological systems is investigated. The equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases. Local stability of the constant positive solution is considered. A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given. It is proved that if the diffusion coefficient of the prey with disease is treated as a bifurcation parameter, non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19175.html} }
TY - JOUR T1 - Analysis of a Prey-Predator Model with Disease in Prey AU - Li , Jianjun AU - Gao , Wenjie AU - Sun , Peng JO - Communications in Mathematical Research VL - 1 SP - 27 EP - 40 PY - 2021 DA - 2021/05 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19175.html KW - eco-epidemiology, bifurcation, non-constant positive steady solution. AB -

In this paper, a system of reaction-diffusion equations arising in eco-epidemiological systems is investigated. The equations model a situation in which a predator species and a prey species inhabit the same bounded region and the predator only eats the prey with transmissible diseases. Local stability of the constant positive solution is considered. A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given. It is proved that if the diffusion coefficient of the prey with disease is treated as a bifurcation parameter, non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.

Li , JianjunGao , Wenjie and Sun , Peng. (2021). Analysis of a Prey-Predator Model with Disease in Prey. Communications in Mathematical Research . 26 (1). 27-40. doi:
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