Direct statistical modeling of HIV-1 infection based on a non-Markovian stochastic model

An approach to the numerical modeling of the dynamics of HIV-1 infection based on a non-Markovian stochastic model is presented. In the model, the population dynamics of cells and viral particles are described taking into account the prehistory of their development and transitions between two compartments. An algorithm for direct statistical modeling of the dynamics of the studied populations is developed. Results obtained by studying special cases of the constructed model, including its deterministic analogue, and published clinical data are used for specifying the details of numerical experiments. The eradication probability of HIV-1 infection and the dynamics of typical realizations of population sizes are examined in relation to the initial number of virus particles and parameters of the model.