Abstract. The article is devoted to the application of mathematical modeling methods to create prognostic techniques for HIV + tuberculosis coinfection in persons held in institutions of the penitentiary system. The development of progosis models is important for fulfilling the tasks of preventing infectious diseases, improving the quality of medical care and the timeliness of correcting the treatment tactics, as well as improving the organizational measures. The article describes scientific approaches and methods of mathematical modeling used to solve the described problem: regression, correlation, analysis of variance, logistic regression, hierarchy analysis method, expert judgment method, artificial neural network. A brief description of the main prognostic methods is given, the influence of predictive factors on an unfavorable outcome of the disease is defined. The main prognostically unfavorable factors that have the greatest impact on the unfavorable prognosis of HIV-associated tuberculosis (the presence of active HIV-associated diseases, extensive and chronic forms of tuberculosis, the level of CD4 lymphocytes, high viral load of HIV, and others) are presented. It is concluded that the increase in the incidence of HIV-associated tuberculosis has led to the development of new effective prediction methods in the case of this co-infection. Key words: HIV infection, tuberculosis, mathematical modeling, forecasting.