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

Author

Listed:
  • Igor Sazonov

    (College of Engineering, Swansea University, Bay Campus, Fabian Way, Swansea SA1 8EN, UK)

  • Dmitry Grebennikov

    (Marchuk Institute of Numerical Mathematics of the RAS, 119333 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics at INM RAS, 119333 Moscow, Russia
    Institute for Personalized Medicine, Sechenov First Moscow State Medical University, 119991 Moscow, Russia)

  • Mark Kelbert

    (Department of Statistics and Data Analysis, National Research University Higher School of Economics, 101000 Moscow, Russia)

  • Andreas Meyerhans

    (ICREA, Pg. Lluis Companys 23, 08010 Barcelona, Spain
    Infection Biology Laboratory, Universitat Pompeu Fabra, 08003 Barcelona, Spain)

  • Gennady Bocharov

    (Marchuk Institute of Numerical Mathematics of the RAS, 119333 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics at INM RAS, 119333 Moscow, Russia
    Institute for Personalized Medicine, Sechenov First Moscow State Medical University, 119991 Moscow, Russia)

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.

Suggested Citation

  • Igor Sazonov & Dmitry Grebennikov & Mark Kelbert & Andreas Meyerhans & Gennady Bocharov, 2020. "Viral Infection Dynamics Model Based on a Markov Process with Time Delay between Cell Infection and Progeny Production," Mathematics, MDPI, vol. 8(8), pages 1-21, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1207-:d:387937
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    References listed on IDEAS

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    1. Li, Dongxi & Zhao, Yue & Song, Shuling, 2019. "Dynamic analysis of stochastic virus infection model with delay effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 528(C).
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