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In this paper we introduce randomness into a model of AIDS and condom use through the technique of parameter perturbation which is standard in stochastic population modeling. We show that the model established in this paper possesses non-negative solutions as desired in any population dynamics. We also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment. Our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system. [ABSTRACT FROM AUTHOR]

In this paper, a model of HIV infection taking into account cell-free and cell-to-cell transmissions is investigated under latency. The viral production rate of infectious CD4 T cells and the activation rate of latently infected CD4 T cells play a major role in the evolution of the disease. A system of nonlinear differential equations is derived to capture the dynamics and systematically analyzed thanks to the spectral theory of dynamical systems and a Routh-Hurwitz criterion. In particular, numerical simulations will be performed in order to extract the critical epidemiological features of the solution. [ABSTRACT FROM AUTHOR]