Mathematical modelling in biomedicine
An interdisciplinary study of mathematical modelling of the cardiovascular and immune systems, related diseases and oncological diseases. Research includes the development and analysis of blood clotting models, and a description of the production of thrombin in normal and pathological cases; the study of spatial models of blood clotting based on reaction-diffusion equations and thrombus formation rate, considered as a reaction-diffusion wave. A study is also conducted on mathematical models for the growth of a cancer tumour, taking into account angiogenesis; determination of optimal protocols for drug administration, taking into account the interaction of chemotherapy and angiogenesis. Mathematical models of the immune response to a viral infection are being developed and studied by taking into account viral mutations; the conditions and dynamics of virus evolution are determined; construction and calibration of mathematical models of varying degrees of particularization for a compact description of key processes of regulation of the immune response, taking into account the structure of lymphoid organs. The results obtained during the project have applications in oncology, immunology, and in the field of cardiovascular diseases.