Viral Infection Dynamics Model Based on a MarkovProcess with Time Delay between Cell Infection and Progeny Production

M. Kelbert; Sazonov I.; Bocharov G.; Grebennikov D.; Meyerhans A.

doi:10.3390/math8081207

Publications

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Viral Infection Dynamics Model Based on a MarkovProcess with Time Delay between Cell Infection and Progeny Production

Mathematics. 2020. Vol. 8. No. 8. P. 1207.

Kelbert M., Sazonov I., Bocharov G., Grebennikov D., Meyerhans A.

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.

Priority areas: IT and mathematics

Keywords: Monte-Carlo Method virus dynamics modelling Markov process with delay

Publication based on the results of:

Methods development of the fractional stochastic calculus (2020)

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