In this paper, the author studies a predator-prey model based on epidemic disease. The epidemic disease is described by SEIR (Susceptible-Exposed-Infected-Recovered) and SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) models with a logistic growth function only in the susceptible prey population. The function of response in the predator-prey model is given by a Lotka-Volterra type. Notice, all epidemic models are characterized by the basic reproduction number R_0. This number gives information whether the epidemic can be controlled. In this work, the author introduces two systems of five nonlinear ordinary differential equations which describe the eco-epidemiological model above using the following functions: susceptible prey S(t), exposed prey E(t), infected prey I(t), recovered prey R(t) and predator P(t). The solutions of the systems are studied by proving their positivity and boundedness. A set of equilibrium points is presented and conditions for their existence and stability are analyzed. A formula for the basic reproduction number R_0 is found. Biological interpretation for different equilibria depending on R_0 is discussed. The numerical experiments presented show some differences in the dynamic of all populations when the SEIR and SEIRS epidemic models are used.
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