Modelling the role of delay in blood flow dynamics in human body using delay differential equations

The blood flow dynamics in the human circulatory system , where blood passes through various arteries, capillaries and veins is realistically modelled in this research paper. Several physiological, pathological, or environmental conditions might cause a delay in the passage of blood from arteries to capillaries such as hypotension, atherosclerosis , vascular resistance etc. This delay has been incorporated in this mathematical model. Feasible non-zero equilibrium is calculated and the stability analysis is carried about this equilibrium point. The asymptotic stability is seen for below-critical point value of delay parameter. Hopf-bifurcation through limit cycles is observed when value of delay parameter crosses the critical point. The analytical results are supported by numerical simulation using MATLAB and play a significant role in good health and well-being.