Viral infection dynamics model based on a Markov process with time delay between cell infection and progeny production

Sazonov, Igor; Grebennikov, Dmitry; Kelbert, Mark; Meyerhans, Andreas; Bocharov, Gennady A.

doi:http://dx.doi.org/10.3390/MATH8081207

Viral infection dynamics model based on a Markov process with time delay between cell infection and progeny production

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Sazonov I, Grebennikov D, Kelbert M, Meyerhans A, Bocharov G. Viral infection dynamics model based on a Markov process with time delay between cell infection and progeny production. Mathematics. 2020;8(8):1207. DOI: 10.3390/MATH8081207

Abstract

Many human virus infections including those with the human immunodeficiency virus type 1 (HIV) are initiated by low numbers of founder viruses. Therefore, random effects have a strong influence on the initial infection dynamics, e.g., extinction versus spread. In this study, we considered the simplest (so-called, ‘consensus’) virus dynamics model and incorporated a delay between infection of a cell and virus progeny release from the infected cell. We then developed an equivalent stochastic virus dynamics model that accounts for this delay in the description of the random interactions between the model components. The new model is used to study the statistical characteristics of virus and target cell populations. It predicts the probability of infection spread as a function of the number of transmitted viruses. A hybrid algorithm is suggested to compute efficiently the system dynamics in state space domain characterized by the mix of small and large species densities.