Development and research of blood clotting models and description of thrombin production in normal and pathological (hemophilia) cases; comparison with experimental data. The study of spatial models of blood clotting based on reaction-diffusion equations. The study of the rate of thrombosis, considered as a reaction-diffusion wave. The study of blood clotting in the stream (veins, arteries), determination conditions for normal growth of the clot and excessive growth leading to the development of thrombosis.
The study of mathematical models of cancer growth, taking into account angiogenesis; determination of optimal protocols for drug administration, taking into account the interaction of chemotherapy and angiogenesis. The study of hematological cancers, including multiple myeloma. The study of mutations of malignant cells and the emergence of resistant clones. The study of the interaction of cancer with the body's immune system and the determination of various modes of tumor growth.
Development and study of mathematical models of the immune response to viral infection taking into account mutations of viruses. Determination of the conditions and dynamics of the evolution of viruses. Construction and calibration of mathematical models of various extent of specification for a compact description of key processes of regulation of the immune response, taking into account the structure of lymphoid organs. Investigation of integrative mathematical models of the immune system response to HIV infection on the criterion of controllability and the structure of reachable sets.
List of key publications on the project:
- G. Bocharov, V. Volpert, B. Ludewig, A. Meyerhans. Mathematical Immunology of Virus Infections. Springer, 2018;
- Bocharov, G., Meyerhans, A., Bessonov, N., Trofimchuk, S., Volpert, V. Interplay between reaction and diffusion processes in governing the dynamics of virus infections. Journal of Theoretical Biology, 2018;
- Beuter, A., Balossier, A., Trofimchuk, S., Volpert, V. Modeling of post-stroke stimulation of cortical tissue. Mathematical Biosciences. 2018;
- Belyaev, A.V., Dunster, J.L., Gibbins, J.M., Panteleev, M.A., Volpert, V. Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones. Physics of Life Reviews. 2018;
- Galochkina, T., Marion, M., Volpert, V. Initiation of reaction–diffusion waves of blood coagulation. Physica D: Nonlinear Phenomena. 2018.
- Mathematical modelling in biology and medicine in three priority directions: cardiovascular system, oncological diseases, the immune response and infectious diseases.
- The results obtained in the course of the project have applications in oncology, immunology, and the field of cardiovascular diseases.