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Seminar on mathematical modeling in biology and medicine
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Mathematical modeling in immunology and medicine: basic principles and directions of development G. A. Bocharovabc a Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow b Moscow Center for Fundamental and Applied Mathematics c I. M. Sechenov First Moscow State Medical University |
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Abstract: The main function of the body's immune system is to control and maintain the antigenic homeostasis of the body's internal environment, and above all, to protect against infectious diseases. The course and outcome of infectious diseases in humans and experimental animals are determined by the kinetics of the spread of antigenic disturbances in the body and the development of immunophysiological reactions, as well as external (therapeutic) effects. For their holistic description and analysis, multiphysical mathematical models are needed that detail the cause-and-effect relationships of infectious and immunological processes at different levels of hierarchical organization and spatiotemporal scales, while taking into account the adaptive formation of the immune repertoire as much as possible, as well as the effect of nonlinear multifactorial contours of molecular, cellular-population and systemic-physiological regulation in the body.. The report will examine the fundamental foundations of the construction of mathematical models of immunology and their applications in medicine developed by G.I. Marchuk. The development of this area is associated with the implementation of approaches to modeling and analyzing the processes that determine the functioning of the immune system, taking into account the diverse characteristics of its "complexity" and their evolution. For this purpose, new classes of mathematical and computer models are being considered that describe the structure, regulation, and dynamics of immune responses in normal and infectious diseases. A distinctive feature of the current stage of development of the mathematical description of the immune system is the meaningful modeling of various infectious diseases of humans and experimental animals (HIV-1, SARS-CoV-2, hepatitis B virus, LCMV). The simulation results allow for a deeper understanding of the mechanisms of regulation and pathogenesis, control factors that determine the modes of viral infections and the possibility of their change, as well as to identify molecular biological targets for antiviral therapy and threshold criteria for the effectiveness of vaccination. Funding: The research was supported by the Russian Science Foundation (grant No. 23-11-00116) and the Moscow Center for Fundamental and Applied Mathematics at the Institute of Applied Mathematics of the Russian Academy of Sciences (Agreement with the Ministry of Education and Science of the Russian Federation No. 075-15-2025-347). Language: English |
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