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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 = {Jianjun and Li and and 18210 and and Jianjun Li and Wenjie and Gao and and 18211 and and Wenjie Gao and Peng and Sun and and 18212 and and Peng Sun}, 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.

JianjunLi, WenjieGao & PengSun. (2021). Analysis of a Prey-Predator Model with Disease in Prey. Communications in Mathematical Research . 26 (1). 27-40. doi:
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