Abstract
Mathematical immunology is the branch of mathematics dealing with the application of mathematical methods and computational algorithms to explore the structure, dynamics, organization and regulation of the immune system in health and disease. We review the conceptual and mathematical foundation of modelling in immunology formulated by Guri I. Marchuk. The current frontier studies concerning the development of multiscale multiphysics integrative models of the immune system are presented.
Acknowledgment
We thank Andreas Meyerhans for fruitful discussions of various topics of the article and for critically reading this manuscript.
Funding: The reported study was funded by the Russian Science Foundation (grant number 18-11-00171) (Sections 3.1–3.3) and by RFBR (project number 20-01-00352) (Sections 1, 2, and 3.4). G. A. Bocharov, D. S. Grebennikov, and R. S. Savinkov were partly supported by Moscow Center for Fundamental and Applied Mathematics (agreement with the Ministry of Education and Science of the Russian Federation No. 075-15-2019-1624). R. S. Savinkov was partly supported by the RUDN University Program 5-100.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Preface
- Methods of variational data assimilation with application to problems of hydrothermodynamics of marine water areas
- Mathematical immunology: from phenomenological to multiphysics modelling
- Iterative solution methods for elliptic boundary value problems
- Multi-physics flux coupling for hydraulic fracturing modelling within INMOST platform
- Tensor decompositions and rank increment conjecture
- Global optimization based on TT-decomposition
Articles in the same Issue
- Frontmatter
- Preface
- Methods of variational data assimilation with application to problems of hydrothermodynamics of marine water areas
- Mathematical immunology: from phenomenological to multiphysics modelling
- Iterative solution methods for elliptic boundary value problems
- Multi-physics flux coupling for hydraulic fracturing modelling within INMOST platform
- Tensor decompositions and rank increment conjecture
- Global optimization based on TT-decomposition