### Mathematical modelling of the dynamics of AIDS epidemics development in the world

#### Abstract

In this work, mathematical modelling of the dynamics of AIDS epidemics development in the world is performed for the following countries: Russian Federation, Austria, France and Brazil. HIV infection and AIDS are the diseases for which the development is under special control of international community. Annual HIV infection morbidity is up to 3 million cases a year, and the average age of the infected varies over the range of 20-30 years. At the moment, there is no cure for HIV infection. Without supporting treatment, it leads to the development of acquired immune deficiency syndrome (AIDS) and death. Consequently, the spreading of HIV leads to serious economic loss. Mathematical methods are widely applied to the analysis of HIV spreading, forecasting the epidemic development and qualitative evaluation of measure effectiveness. Mathematical description of the HIV epidemic development process allows analyzing the character of the disease for each region deeper, perform the comparative study of statistical and modelled data, make suggestions on further possibilities of HIV infection development and confirm the importance of introducing federal measures of confronting human immunodeficiency viruses. Therefore, authors provide the results of analyzing statistical data for the counties mentioned above, mathematical models of AIDS epidemic development and results of modelling for each region. Over the course of this work, optimal parameter values have been found for an accurate description of statistical data. A comparative study of the current situation for AIDS epidemic in Russian Federation, Austria, France and Brazil. As a result, the conclusion of effectiveness of present measures of confronting HIV infection in these countries.

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