Ergodic stationary distribution of age-structured HBV epidemic model with standard incidence rate.

In this article, an S V I R age structure model is formulated that describes the dynamics of the Hepatitis B virus (HBV), keeping in view the vaccinated population and the standard incidence rate. After the formulation of the deterministic system, the model is extended to a stochastic system, taking into account the noises in the transmission coefficient. Utilizing the well-known formula of Itô's and the Lyapunov function theory, first, demonstrate that the perturbed system has a unique global positive solution subject to positive initial conditions. Analyze the model for the extinction of HBV, and the required condition is derived. The threshold parameter for the model is calculated, and by using this quantity, it is proved that for small values of the white noises and R s < 1 , the disease will eventually go extinct at a negative exponential rate. It is also proved that for R s 0 > 1 , the weak permanence of the disease is observed. The criterion R s 0 > 1 confirms the stationary distribution of mean infected persons, suggesting that the illness will remain throughout time. To reinforce the primary analytical findings of this paper, various illustrative examples are conducted separately through numerical simulations. [ABSTRACT FROM AUTHOR]