Calculating the expected time to eradicate HIV-1 using a Markov Chain.

In this study, the expected time required to eradicate HIV-1 completely was found as the conditional absorbing time in a finite state space continuous-time Markov chain model. The Markov chain has two absorbing states: one corresponds to HIV eradication and another representing the possible disaster. This method allowed us to calculate the expected eradication time by solving systems of linear equations. To overcome the challenge of huge dimension of the problem, we applied a novel stop and resume technique. This technique also helped to stop the numerical computation whenever we wanted and continue later from that point until the final result was obtained. Our numerical study showed the dependence of the expected eradication time of HIV on the half-life of the latently infected cells and there agreed with the previous studies. The study predicted that when the half-life of the latent cells varied from 4.6 to 60 months, it took a mean 4.97 to 31.04 years with a corresponding standard deviation of 0.64 to 3.99 years to eradicate the latent cell reservoir. It also revealed the crucial dependence of eradication time on the initial number of latently infected cells.