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Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

Published online by Cambridge University Press:  06 June 2012

P.S. Mandal  and
M. Banerjee
P.S. Mandal
Affiliation:
Department of Mathematics and Statistics Indian Institute of Technology, Kanpur Kanpur - 208016, INDIA
M. Banerjee*
Affiliation:
Department of Mathematics and Statistics Indian Institute of Technology, Kanpur Kanpur - 208016, INDIA
*
⋆ Corresponding author. E-mail: malayb@iitk.ac.in
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Abstract

An eco-epidemiological model of susceptible Tilapia fish, infected Tilapia fish and Pelicans is investigated by several author based upon the work initiated by Chattopadhyay and Bairagi (Ecol. Model., 136, 103–112, 2001). In this paper, we investigate the dynamics of the same model by considering different parameters involved with the model as bifurcation parameters in details. Considering the intrinsic growth rate of susceptible Tilapia fish as bifurcation parameter, we demonstrate the period doubling route to chaos. Next we consider the force of infection as bifurcation parameter and demonstrate the occurrence of two successive Hopf-bifurcations. We identify the existence of backward Hopf-bifurcation when the death rate of predators is considered as bifurcation parameter. Finally we construct a stochastic differential equation model corresponding to the deterministic model to understand the role of demographic stochasticity. Exhaustive numerical simulation of the stochastic model reveals the large amplitude fluctuation in the population of fish and Pelicans for certain parameter values. Extinction scenario for Pelicans is also captured from the stochastic model.

Keywords

Eco-epidemiologystabilityHopf-bifurcationchaosstochasticityextinction
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 3: Epidemiology , 2012 , pp. 99 - 116
Copyright
© EDP Sciences, 2012

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