Regulation of Organism's Antiviral Immune Response: Mathematical Model, Qualitative Analysis, Results
Petr V. Trusov, Nina V. Zaitseva, Vladimir M. Chigvintsev, Dmitriy V. Lanin
Federal Scientific Center for Medical and Preventive Health Risk Management Technologies
Perm National Research Polytechnic University
Perm State University
Abstract. To know the processes occurring in the neuroendocrine and immune system, the complex and branching regulation mechanisms should be taken into account. Most of the studies in this area are dedicated to the biological and mathematical description of individual parts of the regulatory mechanisms, and it greatly facilitates the understanding of the phenomena being studied. But there is a lack of comprehensive description of the processes and internal communications. In the present article, a mathematical model for describing the antiviral immune response is considered taking into account the interacting regulatory influences of the immune and neuroendocrine systems. To describe the innate immunity, the proposed model uses parameters reflecting quantitative measures of the interferon concentration (the inductor of resistance to the infection of target organ cells) and NK-cells (responsible for removing of the infected cells). The simulation of acquired immunity is performed using parameters characterizing the concentration of virus-specific cytotoxic T cells and antibody-forming B lymphocytes. The regulatory mechanisms considered in the model cover the influence of the hypothalamic-pituitary-adrenal axis and the populations of the T-helper cells. The model is developed within the framework of the concept of a multi-level model of the human body, taking into account the interactions between systems and the functional state of the organs included in the review. The model also takes into account the spatial organization of immune and infectious processes in various organs and tissues, for which the delay time of interaction of the components is introduced. The model includes a system of 18 ordinary differential equations with a delayed argument, the parameters of which characterize the rates of various processes that affect the dynamics of infection. The parameters are identified according to published experimental data describing the process of infection of the body with a virus. The dynamics of the immune and neuroendocrine systems under viral infection was calculated, taking into account the disturbance of the synthetic function of the bone marrow. The study provides a qualitative picture of the biological factors that can explain the kinetics of the development of a viral infection.
Key words: mathematical model, dynamic system, virus disease, inborn immunity, acquired immunity, neuroendocrine regulation.