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Regular version of the site

Article

Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics

Mathematical Modelling of Natural Phenomena. 2017. Vol. 12. No. 5. P. 63-77.
Kelbert M., Sazonov I., Bocharov G., Grebennikov D.

Many human infections with viruses such as human immunode ciency virus type 1
(HIV{1) are characterized by low numbers of founder viruses for which the random effects and
discrete nature of populations have a strong effect on the dynamics, e.g., extinction versus spread.
It remains to be established whether HIV transmission is a stochastic process on the whole. In
this study, we consider the simplest (so-called, 'consensus') virus dynamics model and develop a
computational methodology for building an equivalent stochastic model based on Markov Chain
accounting for random interactions between the components. The model is used to study the
evolution of the probability densities for the virus and target cell populations. It predicts the
probability of infection spread as a function of the number of the transmitted viruses. A hybrid
algorithm is suggested to compute efficiently the dynamics in state space domain characterized
by a mix of small and large species densities.