The main function of human cardiovascular system is to maintain adequate blood to different regions of the body. This function is based on the interaction of a number of factors including cardiac output, partial pressures of carbon dioxide  and oxygen  Blood flow through the lungs and tissues is also important for the human respiratory system. Oxygen is transported to tissues while carbon dioxide is transported away from them. This transport depends on two factor: Cardiac output and blood flow. Although the natural state is affected during a physical activity, the autoregulation mechanism tries to maintain the cardiovascular-respiratory parameters to their natural physiological states.

The purpose of this paper is to propose a bi-compartmental model for cardiovascular-respiratory mathematical model including delays. A such model allows to determine blood partial pressures according to the heart rate system and the alveolar ventilation. Taking delays into account, qualitative study of equilibrium allows to determine stability and instability regions as well as the existence of limit cycles that are characterized by oscillations.

Performance, against itself and possible accident during the physical activity can be explained by this analysis. Then we present the numerical simulation results that are based on a generic case. They confirm perfectly theoretical results and they show pathological situations.