Abstract. The authors propose and validate the mathematical models for the human body adaptation mechanisms to oxygen lack in highland and strenuous physical activity. The computer analysis of joint operation of the respiratory, circulatory, heat exchange functional systems and immune response to viral infection is carried out to reveal the nature of intersystem mechanisms of the interaction of functional systems of the body under extreme environmental conditions.

Keywords: mathematical modeling, optimal control, respiratory, circulatory, and heat exchange functional systems, oxygen insufficiency adaptation mechanisms, immune response.