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Stability analysis for SIS epidemic models with vaccination and constant population size

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  • This paper investigates two types of SIS epidemic model with vaccination and constant population size to determine to the thresholds, equilibria, and stabilities. One of SIS models is a delay differential equations, in which the period of immunity due to vaccination is a constant. Another is an ordinary differential equations, in which the loss of immunity due to vaccination is in the exponent form. We find all of their thresholds respectively, and compare them. The disease-free equilibrium is globally asymptotically stable if the threshold is not greater than one; the endemic equilibrium is globally asymptotically stable if the threshold is greater than one.
    Mathematics Subject Classification: 34D23, 92D30.

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