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Mathematical Eco-Epidemiological Model on Prey-Predator System
Mathematical Modelling and Applications
Volume 5, Issue 3, September 2020, Pages: 183-190
Received: Jun. 2, 2020; Accepted: Jun. 23, 2020; Published: Aug. 20, 2020
Authors
Abayneh Fentie Bezabih, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Geremew Kenassa Edessa, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Wollega University, Nekemte, Ethiopia
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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 Ro=[β (μ3)2] ⁄ [qp2 (qp1Λ - μ1μ3)]. If the basic reproduction number Ro > 1, then the disease is endemic and will persist in the prey species. If the basic reproduction number Ro=1, then the disease is stable, and if basic reproduction number Ro < 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.
Keywords
Mathematical Ecoepidemiology, Prey- Predator System, Stability Analysis, Reproduction Number, Simulation Study
Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Purnachandra Rao Koya, Mathematical Eco-Epidemiological Model on Prey-Predator System, Mathematical Modelling and Applications. Vol. 5, No. 3, 2020, pp. 183-190. doi: 10.11648/j.mma.20200503.17
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