Math. Model. Nat. Phenom.
Volume 7, Number 3, 2012Epidemiology
|99 - 116
|06 June 2012
Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model
Department of Mathematics and Statistics Indian Institute of Technology, Kanpur Kanpur - 208016, INDIA
⋆ Corresponding author. E-mail: firstname.lastname@example.org
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.
Mathematics Subject Classification: 34C23 / 60J25 / 92D25
Key words: Eco-epidemiology / stability / Hopf-bifurcation / chaos / stochasticity / extinction
© EDP Sciences, 2012
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.