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The study of population dynamics models as a part of the life sciences is one of the most important existing areas due to the growing threats to the human health and the environment. The principal interest of our research is connected with three types of topics: 1) mathematical oncology, 2) mathematical theory of viral diseases and 3) eco epidemiology. The main interest within the first topic is focused on studies of mathematical models describing interactions of the cancer cell population with the human immune system under applying some kind of the treatment including immunotherapy, chemotherapy, virotherapy and others. In the second topic we are interested in studies of in-host mathematical models of various viral diseases like HIV infection, pneumonia and others. Our third topic focuses on studying dynamics of populations of prey and predators living in their natural habitat that are susceptible to infectious diseases. From the mathematical point of view, finding conditions for the extinction or persistence of interacting populations is the problem of our principal interest for each of these researching topics. Here in CITEDI we propose to study ultimate dynamics of interacting populations with help of original ideas that date back to works of K.E. Starkov. The core of this approach is based on the idea of the localization of bounded dynamics of a nonlinear multidimensional system of ordinary differential equations. As a result of such analysis, one may find cancer eradication conditions; conditions for successful treatment of infectious diseases or elaborate eco-epidemiological forecast for a habitat which are expressed in terms of model parameters. The most interesting issue in the first two topics is how the disease curing conditions depend on treatment parameters. This gives a chance of a theoretical justification of medical protocols and subsequent application for health prognosis of a patient. The participation in these works will allow you to learn new research methods and may become the beginning of your successful professional and scientific career.
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