A general Markov model of the HIV epidemic in populations involving both sexual contact and IV drug use

In this paper, we develop a general Markov model for the HIV epidemic involving both sexual contact and IV drug use. For this model, we derive the probability generating function of the HIV epidemic and derive equations for the means, the variances and the covariances of the numbers of susceptible people, latent people, infective people and AIDS cases. By using these equations, we generate some simulation studies to illustrate effects of some risk factors on the mean HIV behavior and on the variances and the covariances of the numbers of latent people, infective people and AIDS cases.