Abstract
Environmental factors such as, humidity and temperature pose significant impacts on the dynamics of hepatitis B virus (HBV). The stochastic modeling has been proved to be a powerful tool for revealing such impacts. With this motive, the present study enacts the formulation and analysis of a stochastic hepatitis B model considering a time-delay in the transmission coefficient, and CTL immune response class. Initially, the model is investigated for the existence of a unique global solution. By using the stochastic Lyapunov functional theory, the model was further analyzed for extinction and persistence of the disease. It is evident that the ergodic stationary distribution exists under certain condition. We infer that the white noise plays a significant role in controlling the infection. Relatively large noise guarantees the extinction of HBV. Similarly, it is inferred that the delay factor is responsible for the periodic occurrence and re-infection of the disease. Additionally, for providing a strong support to the theoretical results, sample trajectories were displayed at the end of the study.
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