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The spread of Human Immune deficiency Virus (HIV) and consequent Acquired Immune Deficiency Syndrome (AIDS) has created a pandemic situation in many countries of the world. The HIV is a lentivirus organism that attacks the power of immunity in the human body. It is disheartening to note that there is no proper and definite cure for this infection till this day all the efforts of the scientist in inventing a medicine for this is still in process. One of the models of transmission of HIV from the infected to any other person is by sexual contacts. The transmission of HIV from the infected to the other on successive contacts leads to the contribution of antigenic diversity of the antigen which in turn increases the survival of the antigens. The cumulative contribution to the antigenic diversity of the invading antigen in successive contacts if exceeds a particular level called antigenic diversity threshold then the human immune system is unable to fight against the antigens. The determination of the intensity of antigenic of the intensity of antigenic diversity has been studied by several researchers. Nowak and May (1991) have studied the antigenic diversity. Jewell and Shiboski (1990) have discussed the infectivity of HIV. Kannan et al. (2007) have used a mathematical model to determine the expected time to seroconversion Stilianakis et al. (1994) have discussed on the antigenic diversity threshold model for AIDS. In the model, it is consider that a person takes some precautionary measures to avoid the transmission of HIV and this is called the alertness. However, if a person fails to adopt such preventive measure in other words if the person is in alert then the HIV gets transmitted. So, the model observed here is under the assumption that the transmission of HIV is possible only during the contacts without alertness. A stochastic model for HIV transmission under alertness under the assumption that threshold level of antigenic diversity is a random variable which follows a gamma distribution and exponential geometric distribution has been discussed by Kannan et al. (2007), Kannan and Chandrasekar (2015). The expected time to seroconversion is estimated using transmission probability with threshold of an Erlang truncated exponential distribution. Numerical illustration is also providing.

A Stochastic Approach to Determine Seroconversion Time under Alertness using Erlang Truncated Exponential Distribution