Stochastic Analog of the Dynamic Model of HIV-1 Infection Described by Delay Differential Equations

Abstract

Some deterministic and stochastic models are constructed basing on the same assumptions about the dynamics of HIV-1 infection. The deterministic model has the form of a system of differential equations with three delays. The stochastic model is based on a branching process with the interaction of particles and takes into account the stages of maturation of cells and virions. The durations of these stages correspond to the parameters describing the delays in the deterministic model. The influence of discreteness of stochastic model variables on the dynamics of HIV-1 infection is demonstrated. We find the coinciding and significantly different conditions of HIV-1 infection elimination in the framework of deterministic and stochastic models.