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Analysis of a three species eco-epidemiological model. (English) Zbl 0967.92017
Summary: 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.

MSC:
92D40 Ecology
37N25 Dynamical systems in biology
34D05 Asymptotic properties of solutions to ordinary differential equations
92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
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