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Modelling of Human Infections

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Mathematical Immunology of Virus Infections

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Abstract

In this chapter, we illustrate the application of mathematical models and computational analyses tools of various complexities to the description and explanation of some observed phenotypes of viral infections in humans, such as HIV and HBV infections. Specifically, we try to gain a deeper understanding of the sensitivity of infection dynamics to growth rate and the efficacy of antigen presentation by APCs, the phenomenon of spontaneous recovery from HBV infection, and the kinetic determinants of a low-level (i.e. below the detection threshold) HBV persistence. The material of this chapter is based on our previous work published in [3, 12,13,14, 33].

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Notes

  1. 1.

    Material of this section uses the results of our studies from AIDS Res Hum Retroviruses, Vol. 23, Sester et al., Maintenance of HIV-Specific Central and Effector Memory CD4 and CD8 T Cells Requires Antigen Persistence, Pages 549–553, Copyright \(\copyright \) 2007 Mary Ann Liebert, Inc.

  2. 2.

    Material of Sects. 5.3.1 and 5.3.2 uses the results of our studies from Journal of Virology, Vol. 78, Bocharov et al., Underwhelming the immune response: effect of slow virus growth on CD8+-T-lymphocyte responses, Pages 2247–2254, Copyright \(\copyright \) 2004 by the American Society for Microbiology. Material of Sect. 5.3.3 uses the results of our studies from Journal of Computational and Applied Mathematics, Vol. 184, Luzyanina et al., Numerical bifurcation analysis of immunological models with time delays, Pages 165–176, Copyright \(\copyright \) 2005, with permission from Elsevier.

  3. 3.

    Material of this section uses the results of our studies from Journal of Computational and Applied Mathematics, Vol. 184, Luzyanina et al., Numerical bifurcation analysis of immunological models with time delays, Pages 165–176, Copyright \(\copyright \) 2005, with permission from Elsevier.

  4. 4.

    Material of Sect. 5.4 uses the results of our studies from Mathematics and Computers in Simulation, Vol. 96, Luzyanina and Bocharov, Stochastic modeling of the impact of random forcing on persistent hepatitis B virus infection, Pages 54–65, Copyright \(\copyright \) 2014, with permission from Elsevier.

  5. 5.

    Material of Sect. 5.5 uses the results of our studies from Journal of Computational and Applied Mathematics, Vol. 184, Marchuk et al., Adjoint equations and analysis of complex systems: Application to virus infection modelling, Pages 177–204, Copyright \(\copyright \) 2005, with permission from Elsevier.

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Author information

Authors and Affiliations

  1. Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

    Gennady Bocharov

  2. Institut Camille Jordan, UMR 5208 CNRS, Centre National de la Recherche Scientifique (CNRS), Villeurbanne, France

    Vitaly Volpert

  3. RUDN University, Moscow, Russia

    Vitaly Volpert

  4. Institute of Immunobiology, Kantonsspital St. Gallen, St. Gallen, Switzerland

    Burkhard Ludewig

  5. Parc de Recerca Biomedica Barcelona, ICREA and Universitat Pompeu Fabra, Barcelona, Spain

    Andreas Meyerhans

Authors
  1. Gennady Bocharov
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  2. Vitaly Volpert
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  3. Burkhard Ludewig
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  4. Andreas Meyerhans
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Correspondence to Gennady Bocharov .

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Bocharov, G., Volpert, V., Ludewig, B., Meyerhans, A. (2018). Modelling of Human Infections. In: Mathematical Immunology of Virus Infections. Springer, Cham. https://doi.org/10.1007/978-3-319-72317-4_5

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