Science Journal of Applied Mathematics and Statistics 2021; 9(1): 1-14 http://www.sciencepublishinggroup.com/j/sjams doi: 10.11648/j.sjams.20210901.11 ISSN: 2376-9491 (Print); ISSN: 2376-9513 (Online) Eco-Epidemiological Modelling and Analysis of Prey-Predator Population Abayneh Fentie Bezabih * , Geremew Kenassa Edessa, Koya Purnachandra Rao Department of Mathematics, Wollega University, Nekemte, Ethiopia Email address: * Corresponding author To cite this article: Abayneh Fentie Bezabih, Geremew Kenassa Edessa, Koya Purnachandra Rao. Eco-Epidemiological Modelling and Analysis of Prey- Predator Population. Science Journal of Applied Mathematics and Statistics. Vol. 9, No. 1, 2021, pp. 1-14. doi: 10.11648/j.sjams.20210901.11 Received: November 10, 2020; Accepted: December 4, 2020; Published: February 23, 2021 Abstract: In this paper, prey-predator model of five Compartments are constructed with treatment is given to infected prey and infected predator. We took predation incidence rates as functional response type II and disease transmission incidence rates follow simple kinetic mass action function. The positivity, boundedness, and existence of the solution of the model are established and checked. Equilibrium points of the models are identified and Local stability analysis of Trivial Equilibrium point, Axial Equilibrium point, and Disease-free Equilibrium points are performed with the Method of Variation Matrix and Routh Hourwith Criterion. It is found that the Trivial equilibrium point   is always unstable, and Axial equilibrium point   is locally asymptotically stable if βk - (t 1 +d 2 ) < 0, qp 1 k - d 3 (s+k) < 0, & qp 3 k - (t 2 +d 4 )(s+k) < 0 conditions hold true. Global Stability analysis of endemic equilibrium point of the model has been proved by Considering appropriate Liapunove function. In this study, the basic reproduction number of infected prey is obtained to be the following general formula R 01 =[(qp 1 -d 3 ) 2 kβd 3 s 2 ]⁄[(qp 1 -d 3 ){(qp 1 -d 3 ) 2 ks(t 1 +d 2 )+rsqp 2 (kqp 1 -kd 3 -d 3 s)}] and the basic reproduction number of infected predator population is computed and results are written as the general formula of the form as R 02 =[(qp 1 -d 3 )(qp 3 d 3 )k+αrsq(kqp 1 -kd 3 -d 3 s)]⁄[(qp 1 -d 3 ) 2 (t 2 +d 4 )k]. If the basic reproduction number is greater than one, then the disease will persist in prey-predator system. If the basic reproduction number is one, then the disease is stable, and if basic reproduction number less than one, then the disease is dies out from the prey-predator system. Finally, simulations are done with the help of DEDiscover software to clarify results. Keywords: Eco-Epidemiology, Prey-Predator, Stability, Variation Matrix, Reproduction Number, Simulation 1. Introduction Mathematical Modeling of prey-predator systems of interaction of species have a long history since original remarkable work was done by Lotka-Volterra Model in 1920 [1, 3, 5, 6], and SIR model Compartment of systems of population is another vital area of research after pioneering work of Kermack and Mckendrick [1-3, 5-10]. Anderson and May where the first who combined these two modeling systems, while Chattopadhyay and Arino were the first who used the term ''eco-epidemiology'' for such models [3, 5, 7]. The dynamics of disease in prey-predator systems now become an interesting area of research due to the fact that prey-predator interaction is rich and complex in nature [4, 6, 7, 11-13]. Several mathematical models have been proposed and studied on prey-predator systems [1-7, 9-12]. Many studies focused on the study of disease in a prey only [1-5, 7, 12], other researchers were interested in the study of disease within the predator population only [14], and there are also some studies on diseases in both prey and predators [6, 9, 11] In this paper, we proposed and studied infectious disease on both prey and predator interaction of species with treatment given to infected prey and infected predator. 2. Model Formulation and Assumptions In this paper, the prey-predator population divided into five compartments. let us denote X(t)-Susceptible prey,  - infected prey,  -Susceptible predator,  - infected predator,   both infected prey and infected predator population under treatment. In the absence of infectious disease, the susceptible prey population grows logistically with intrinsic