Abstract
This paper presents infectious disease in prey-predator system. In the present work, a three Compartment mathematical eco-epidemiology model consisting of susceptible prey- infected prey and predator are formulated and analyzed. The positivity, boundedness, and existence of the solution of the model are proved. Equilibrium points of the models are identified. Local stability analysis of Trivial, Axial, Predator-free, and Disease-free Equilibrium points are done with the concept of Jacobian matrix and Routh Hourwith Criterion. Global Stability analysis of endemic equilibrium point of the model has been proved by defining appropriate Liapunove function. The basic reproduction number in this eco-epidemiological model obtained to be <i>R<sub>o</sub>=[β (μ<sub>3</sub>)<sup>2</sup>] ⁄ [qp<sub>2</sub> (qp<sub>1</sub>Λ - μ<sub>1</sub>μ<sub>3</sub>)]</i>. If the basic reproduction number <i>R<sub>o</sub></i> > 1, then the disease is endemic and will persist in the prey species. If the basic reproduction number <i>R<sub>o</sub></i>=1, then the disease is stable, and if basic reproduction number <i>R<sub>o</sub></i> < 1, then the disease is dies out from the prey species. Lastly, Numerical simulations are presented with the help of DEDiscover software to clarify analytical results.
Highlights
Mathematical Ecology and Mathematical epidemiology are two major fields in the study of biology and applied mathematics
The infected and susceptible prey are decreasing in the graph due to prey is suffering from predation and infectious disease for some time
The total preypredator population indicate oscillations and after some time the population of prey species are minimize in number or remain stable depending on the situation of the populations
Summary
Mathematical Ecology and Mathematical epidemiology are two major fields in the study of biology and applied mathematics. These diseases often play an important roles in regulating the population sizes [1, 5, 10, 12, 13] Mathematical study of such populations has attracted attentions of both ecologists and mathematicians from several years past. As a result numerous mathematical models have been developed, and these models have become essential tools in analyzing the interaction of different populations, the interaction between prey and predator [10, 12, 15, 17]. The effect of disease in ecological system is Abayneh Fentie Bezabih et al.: Mathematical Eco-Epidemiological Model on Prey-Predator System an important issue from a mathematical as well as an ecological point of view.
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