A stochastic model for estimation of expected time to seroconversion of HIV infected using exponential-geometric distribution

This paper focuses on the study of a stochastic model for predicting the seroconversion time of HIV transmission. The estimation of expected time to seroconversion of HIV infected over the time interval (0, t], is an important aspects which helps medical intervention. The time to seroconversion from the point of infection depends upon what is known as antigenic diversity which acts against the immune ability of an individual. If the antigenic diversity causes a particular level which is known as the antigenic diversity threshold, the immune system collapses and seroconversion take places. In this paper, the stochastic model for the estimation of expected time to seroconversion is derived under the assumption that threshold level of antigenic diversity is a random variable which follows exponential-geometric distribution. The mean time to seroconversion and its variance are derived and the numerical illustrations are provided.