Analysis of a Three Species Eco-Epidemiological Model1

This paper formulates and analyzes a predator prey model with disease in the prey. Mathematical analyses of the model equations with regard to invariance of nonnegativity, boundedness of solutions, nature of equilibria, permanence, and global stability are analyzed. It is also shown that for some parameter values, the positive equilibrium is asymptotically stable, but for other parameter values, it is unstable and a surrounding periodic solution appears by Hopf bifurcation. A concluding discussion with numerical simulation is then presented.