Propagation of disease from exotic infected predator to native population-A prey predator model

Chanda Purushwani; Poonam Sinha

doi:10.26637/MJM0603/0029

Abstract

In this paper, a prey predator model for native population with SI infection in exotic population is developed and analyzed. A model with prey predator interaction in native population and exotic predator having the risk of infection is suggested to observe the transmission of disease from exotic predators to native population. Disease free equilibrium points (in presence and absence of predator) and endemic equilibrium points are calculated. Conditions for the existence and boundedness of equilibrium points have been derived. The local stability analysis of the model system around the all biologically feasible equilibrium points is discussed. We perform global dynamics of the model using Lyapunov theorem for endemic equilibrium point. We compare the growth of population in terms of ecological sensitive parameters predation rate $\left(\eta_3\right)$, carrying capacity of environment $(K)$ and transmission rate of disease $(\beta)$ with the help of suitable graphs.

Keywords:

Prey predator model, Stability Analysis, Descartes’ rule of signs, SI model, Hurwitz criteria and Lyapunov theorem

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Chanda Purushwani Department of Mathematics, S. M. S. Government Model Science College, Gwalior- 474010, M. P., India.
Poonam Sinha Department of Mathematics, S. M. S. Government Model Science College, Gwalior- 474010, M. P., India.

Pages: 648-657
Date Published: 01-07-2018
Vol. 6 No. 03 (2018): Malaya Journal of Matematik (MJM)

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