On the Stability Analysis for the Stochastic SVIR Model with Vaccination Age

The stochastic bifurcations of the infectious model with vaccination age are studied in this paper. It should be noted that biological parameters such as infectious and recovery rates randomly fluctuate by the random noise caused by environmental changes and individual differences. Moreover, since the effectiveness of vaccination varies greatly depending on vaccination age, we propose the stochastic infectious disease model with vaccination age. The prevalence of infectious diseases is closely related to the stability of the two types of the steady states, the disease-free state (DFS) and the endemic steady one (ES), of the infectious disease model. Hence, we study the stability of the DFS and the ES using the stochastic stability analysis and the bifurcation theory. By numerical simulations, we consider the influence of the random noise on the stability of the DFS and the ES.