Propagation of disease from exotic infected predator to native population-A prey predator model
Authors :
Chanda Purushwani1* and Poonam Sinha2
Author Address :
1,2Department of Mathematics, S. M. S. Government Model Science College, Gwalior- 474010, M. P., India.
*Corresponding author.
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 $left(eta _{3} ight),$ carrying capacity of environment $left(K ight)$ and transmission rate of disease $left(eta ight)$ with the help of suitable graphs.
Keywords :
Prey predator model, SI model, Stability Analysis, Descartes’ rule of signs, Hurwitz criteria and Lyapunov theorem.
DOI :
Article Info :
Received : July 07, 2018; Accepted : September 22, 2018.
