Application of stochastic Model For The Distribiution HIV Latency Time Based on T4 Count

A mathematical model is proposed for the description of the T4 level, as a function of the since initial infection, in the blood of an HIV-infected individual. Two random variables are defined for each infected individual, the time T from the moment of infection to the moment when the infection first discovered, and level R of T4 cells in the blood at the time of discovery. Here T is the length of the latency period, and is not typically observable. On the basis of a stochastic model employing a stationary Gaussian process, the joint density of this two random variables is derived, and hence the conditional distribution of T. given R. It is shown that if T has an exponential marginal distribution, then the conditional distribution of T is a censored normal distribution. The theory is applied to data collected from intravenous drug users in New York City. We applied this theory to real data of infected individual in Kermanshah and estimated this model on this data.