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Global stability results in a SVIR epidemic model with immunity loss rate depending on the vaccine-age. (English) Zbl 1470.92335

Summary: We formulate a susceptible-vaccinated-infected-recovered (SVIR) model by incorporating the vaccination of newborns, vaccine-age, and mortality induced by the disease into the SIR epidemic model. It is assumed that the period of immunity induced by vaccines varies depending on the vaccine-age. Using the direct Lyapunov method with Volterra-type Lyapunov function, we show the global asymptotic stability of the infection-free and endemic steady states.

MSC:

92D30 Epidemiology
34K20 Stability theory of functional-differential equations
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