A Stochastic Model With Antigenic Diversity Threshold Of Hiv Transmission Using Smallest Order Statistics

This paper focuses on the study of a stochastic model for predicting the excepted time to cross the antigenic diversity threshold of HIV infected using the intercontact time between the successive contact forms an order statistics. In the estimation of excepted time to seroconversion, there is an important role for the interarrival time between successive contact and its has a significance influence. We propose the stochastic model assuming the intercontact time between successive contact from a smallest order statistics and threshold distribution is Generalized Rayleigh Distribution. The mean time to seroconversion and its variance are derived and numerical illustrations are provided.