Title: Mathematical modelling of prey-predator interaction with disease in prey

Authors: Mini Ghosh; Xue-Zhi Li

Addresses: School of Advanced Sciences, VIT University, Chennai Campus, Chennai-600127, India ' Department of Mathematics, Xinyang Normal University, Xinyang 464000, China

Abstract: This paper presents a nonlinear mathematical model of prey-predator interaction in which the prey is infected by an infectious disease while assuming that the disease is not transmitted to predator though the rates of predation can be different for the susceptible and infected preys. We also assume that only susceptible prey population contributes in the reproduction. The infective population competes with susceptible population to population growth towards the carrying capacity and here the disease transmission follows the standard incidence. The basic reproduction numbers both in absence and presence of the predator are computed and the equilibria of the mathematical model are obtained. Our results show that there is a possibility of two coexistence equilibria for some set of parameters but only one of them can be locally asymptotically stable. We also observed that the system undergoes 'Hopf-bifurcation' when the maximum predation rate β crosses a threshold value. Finally, the numerical simulation is performed and that supports the analytical findings.

Keywords: predator-prey interaction; reproduction number; Hopf bifurcation; numerical simulation; mathematical modelling; infectious diseases; nonlinear modelling; disease transmission; predation rate.

DOI: 10.1504/IJCSM.2016.080075

International Journal of Computing Science and Mathematics, 2016 Vol.7 No.5, pp.443 - 458

Received: 26 Feb 2014
Accepted: 18 Jan 2015
Published online: 01 Nov 2016 *

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