Seroconversion of Hiv infected when virulence threshold undergoes changes

The progression of the HIV infection is indicated by seroconversion. Hence, the seroconversion of an individual with HIV infection is a vital event. The seroconversion occurs due to contribution to the antigenic diversity of the antigens due to successive sexual contacts the seroconversion occurs as and when the total antigenic diversity crosses the antigenic diversity threshold. Virulence also contributes to the seroconversion and the virulence gained due to successive contacts, when exceeds the virulence threshold the seroconversion occurs. In this paper it is assumed that the virulence threshold is a random variable which under goes a parametric change after a truncation point. Using this property the expected time to seroconversion and its variance are derived. Numerical illustration is also provided.