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On a nonautonomous SEIRS model in epidemiology. (English) Zbl 1245.34040
Summary: We derive some threshold conditions for permanence and extinction of diseases that can be described by a nonautonomous SEIRS epidemic model. Under the quite weak assumptions, we establish some sufficient conditions to prove the permanence and extinction of disease. Some new threshold values are determined.

MSC:
34C11 Growth and boundedness of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
92D30 Epidemiology
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