A stochastic model to estimate the expected time to seroconversion of HIV infected

The incidence and spread of HIV infection all over the world has created a pandemic situation. The impact of this infection and its spread is not only on the affected individuals but also for the government and social organizations. The antigenic diversity of the HIV plays a major role in the progression of the infection. Several mathematical and stochastic models have been developed by researchers in this area. A particular aspect of study is to estimate the expected time to cross the antigenic diversity threshold. When the antigenic diversity crosses a particular level called the antigenic diversity threshold the seroconversion occurs. In this paper a stochastic model is developed under the assumption that the threshold level which is a random variable undergoes a parametric change after crossing a truncation point. The expected time to seroconversion is estimated and its variance is also found out using the shock model and cumulative damage concept.