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The asymptotic behavior of a nonautonomous eco-epidemic model with disease in the prey. (English) Zbl 1202.34098

Summary: A nonautonomous eco-epidemic model with disease in the prey is formulated and studied. Some sufficient and necessary conditions on the permanence and extinction of the infective prey are established by introducing the new research method. Some sufficient conditions on the global attractivity of the model are presented by constructing a Lyapunov function. Finally, an example is given to show that the periodic model is global attractivity if the infective prey is permanent.

MSC:

34D20 Stability of solutions to ordinary differential equations
92D30 Epidemiology
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