A semi-stochastic model for HIV population dynamics

A semi-stochastic model is developed and investigated for human immunodeficiency virus type-1 (HIV-1) population dynamics. The model includes both stochastic parts (changes of CD4+ T cells) and deterministic parts (changes of free virions). Using the best currently available parameter values, we estimate the distributions of the time of occurrence and the magnitude of the early peak in virions. We investigated the effects of varying parameter values on mean solutions in order to assess the stochastic effects of between-patient variability. Numerical simulation shows that the lower the infection rate, the higher the death rate of the infected cells, more rapid clearance of virions and lower rate of virion emission by the infected cells result in lower speed of infection progression and magnitude but a greater variability in response. We also examine the probability that a small viral inoculum fails to establish an infection. Further, we theoretically quantify the expected variability around the infected equilibrium for each population by using diffusion approximation.