Eco-Epidemiological Modelling and Analysis of Prey-Predator Population

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 〖E〗_(o) is always unstable, and Axial equilibrium point 〖E〗_(A) is locally asymptotically stable if βk - (t1+d2) < 0, qp1k - d3(s+k) < 0, & qp3k - (t2+d4)(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 R01=[(qp1-d3)2 kβd3s2]⁄[(qp1-d3){(qp1-d3)2ks(t1+d2 )+rsqp2 (kqp1-kd3-d3s)}] and the basic reproduction number of infected predator population is computed and results are written as the general formula of the form as R02=[(qp1-d3 )(qp3 d3 )k+αrsq(kqp1-kd3-d3s)]⁄[(qp1-d3)2 (t2+d4)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.