Permanence and extinction for a nonautonomous SVIR epidemic model with distributed time delay∗


In this paper we have considered a nonautonomous SV IR epidemic model with varying total population size and distributed time delay to become infectious. Instead of assuming that vaccinees gain immunity immediately, we have assumed that they are different from susceptible and recovered persons and it takes some time for them to gain immunity and then enter into the recovered class. Here, we have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical technique. We have obtained the explicit formula of the eventual lower bound of infected persons. We have introduced some new threshold values R0 and R∗ and further obtained that the disease will be permanent when R0 > 1 and the disease will be going to extinct when R∗ < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. In special case, our model reduces to the standard SIRS model without vaccination with the classical basic reproduction number. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness.

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@inproceedings{Samanta2010PermanenceAE, title={Permanence and extinction for a nonautonomous SVIR epidemic model with distributed time delay∗}, author={Guruprasad Samanta}, year={2010} }