An ecoepidemic model with prey herd behavior and predator feeding saturation response on both healthy and diseased prey

M Banerjee, B.W. Kooi, E. Venturino

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

A predator-prey system is analysed where the transmissible disease can spread into the prey population. This will lead to a three-dimensional ecoepidemic model described by the temporal change of the healthy and diseased prey and the predator populations. The predator-prey interaction is modelled using the square root functional response such that the prey experience group defence: only the healthy individuals at the edge of the herd are consumed while the infected drift behind the herd. The predator feeds on both healthy and diseased prey individuals. The two prey populations are assumed substitutable so that a deficiency in one of the prey populations can be compensated by consuming the other. The resulting model for the trophic interaction is an extension of the classical Holling type II functional response for one prey population. Bifurcation analysis gives long-term dynamics of the boundary and interior equilibria, limit cycles and heteroclinic connections to saddle equilibria. The main goal is to gain insight into the effects of simultaneous predator feeding of both healthy and diseased individuals on the dynamics of the predator-prey system. With simultaneous feeding the feasibility of the system becomes smaller.
Original languageEnglish
Pages (from-to)133-161
JournalMathematical Modelling of Natural Phenomena
Volume12
Issue number2
DOIs
Publication statusPublished - 21 Apr 2017

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Predator prey systems
Predator
Prey
Saturation
Functional Response
Predator-prey System
Model
Heteroclinic Connection
Predator-prey
Bifurcation Analysis
Saddle
Interaction
Square root
Limit Cycle
Interior
Three-dimensional

Cite this

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title = "An ecoepidemic model with prey herd behavior and predator feeding saturation response on both healthy and diseased prey",
abstract = "A predator-prey system is analysed where the transmissible disease can spread into the prey population. This will lead to a three-dimensional ecoepidemic model described by the temporal change of the healthy and diseased prey and the predator populations. The predator-prey interaction is modelled using the square root functional response such that the prey experience group defence: only the healthy individuals at the edge of the herd are consumed while the infected drift behind the herd. The predator feeds on both healthy and diseased prey individuals. The two prey populations are assumed substitutable so that a deficiency in one of the prey populations can be compensated by consuming the other. The resulting model for the trophic interaction is an extension of the classical Holling type II functional response for one prey population. Bifurcation analysis gives long-term dynamics of the boundary and interior equilibria, limit cycles and heteroclinic connections to saddle equilibria. The main goal is to gain insight into the effects of simultaneous predator feeding of both healthy and diseased individuals on the dynamics of the predator-prey system. With simultaneous feeding the feasibility of the system becomes smaller.",
author = "M Banerjee and B.W. Kooi and E. Venturino",
year = "2017",
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An ecoepidemic model with prey herd behavior and predator feeding saturation response on both healthy and diseased prey. / Banerjee, M; Kooi, B.W.; Venturino, E.

In: Mathematical Modelling of Natural Phenomena, Vol. 12, No. 2, 21.04.2017, p. 133-161.

Research output: Contribution to JournalArticleAcademicpeer-review

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AB - A predator-prey system is analysed where the transmissible disease can spread into the prey population. This will lead to a three-dimensional ecoepidemic model described by the temporal change of the healthy and diseased prey and the predator populations. The predator-prey interaction is modelled using the square root functional response such that the prey experience group defence: only the healthy individuals at the edge of the herd are consumed while the infected drift behind the herd. The predator feeds on both healthy and diseased prey individuals. The two prey populations are assumed substitutable so that a deficiency in one of the prey populations can be compensated by consuming the other. The resulting model for the trophic interaction is an extension of the classical Holling type II functional response for one prey population. Bifurcation analysis gives long-term dynamics of the boundary and interior equilibria, limit cycles and heteroclinic connections to saddle equilibria. The main goal is to gain insight into the effects of simultaneous predator feeding of both healthy and diseased individuals on the dynamics of the predator-prey system. With simultaneous feeding the feasibility of the system becomes smaller.

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