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A Kind of SIS Epidemic Model with Periodic Parameters
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O175.12

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    Abstract:

    The spread of some communicable diseases often has a certain periodicity. By incorporating the periodic parameters of disease transmission into the classical SIS epidemic model, an SIS epidemic model with periodic parameters is established. By means of the comparison theorem and the stability theory of ordinary differential equations, the threshold determining whether the disease dies out or not and determining the dynamical behaviors of the model is obtained via qualitative analysis. When the threshold is negative, the disease-free periodic solution of the model is globally asymptotic stable, which implies that the disease dies out eventually. When the threshold is positive, the disease-free periodic solution of the model is unstable, and the model still has a unique endemic periodic solution that is globally stable. This implies that the disease persists in the population, and that the number of the infected individuals will change with a certain periodicity.

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  • Received:
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  • Online: November 24,2015
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