A stochastic Model for early HIV-1 population dynamics

A simple stochastic mathematical model is developed and investigated for ea rly human immunodeficiency virus type-1 (HIV-1) population dynamics. The mo del, which is a multi-dimensional diffusion process, includes activated uni nfected CD4(+) T cells, latently and actively infected CD4(+) T cells and f ree virions occurring in plasma. Stochastic effects are assumed to arise in the process of infection of CD4(+) T cells and transitions may occur from uninfected to latently or actively infected cells by chance mechanisms. Usi ng the best currently available parameter values, the intrinsic variability in response to a given initial infection is examined by solving the stocha stic system numerically. We estimate the statistical distributions of the t ime of occurrence and the magnitude of the early peak in viral concentratio n. The maximum of the viral load has a value in the experimental range and its time of occurrence has a 95% confidence interval from 19.4 to 25.1 days . The stochastic nature of the growth of viral density is extremely pronoun ced in the first few days after initial infection. Threshold effects are no ted at virion levels of about 3-5 x 10(-5) mm(-3). In addition to modeling the intrinsic variability in HIV-1 growth, we have explored the effects of perturbations in the parameter values in order to assess the additional sto chastic effects of between-patient variability. We found that changes in th e initial number of virions or dose size, the rate at which latently infect ed CD4(+) T cells are converted to the actively infected form and the fract ion of latent cells had only minor effects on the size, speed and variabili ty of the response. In contrast, decreased speed and magnitude but greater variability in response were obtained when the death rate of uninfected CD4 (+) T cells, the death rate of actively infected cells and the clearance ra te of the virus were increased or when the appearance rate of uninfected CD 4(+) T cells, the number of virions produced by infected cells, the infecti on rate of CD4(+) T cells and the initial number of uninfected activated CD 4(+) T cells were decreased. We also determined the distribution of the tim e to reach a given virion density. From this distribution the probability o f detection of the virus as a function of time can be estimated. The numeri cal results obtained are in the range of experimental values and are discus sed in relation to recently proposed detection and testing procedures. (C) 1998 Academic Press.