Stochastic dynamics of a Hepatitis B virus transmission model

Hepatitis B is an infectious disease caused by the Hepatitis B virus (HBV) and has caused epidemics in parts of Asia and Africa. During the last two decades, mathematical models have been designed to evaluate the effect of public health programs and provided long-term predictions regarding the disease prevalence and control. These mathematical models are dominantly deterministic because of the large population size. However, when considering elimination and eradication of the HBV, the demographic noise due to the inherent discreteness of individuals may play an important role in determining the dynamics of HBV infection. This work develops a stochastic model to study the influence of small number of infected individuals on the extinction of the disease. Simulation results suggested that, when the infected population size is small, there is disparity between the deterministic model using ordinary differential equations and the corresponding stochastic model. This research work suggested that stochastic modeling could provide a powerful tool to study the eradication of epidemic diseases.