Population model of cardiovascular diseases: Global dynamics, sensitivity analysis, and optimal control

Abstract

Mortality and morbidity due to atherosclerosis are from its tendency to cause cardiovascular diseases (CVDs). Studies have shown that this silent process is facilitated by the associated risk factors. Someone who just experienced a CVDs event already had atherosclerosis long ago, and its rupture causes the blood clot to block the blood flow completely. Here, we investigate the population dynamics of non and post-CVDs individuals with model calibration using the estimated global CVDs-induced death data. In the first, we analyze the basic properties of the governing equations. The model depicted a locally and globally asymptotically stable equilibrium point. Second, we analyze the reasonability of the model by data fitting with the global mortality of CVDs. By computing the sensitivity index on the CVDs equilibrium, we proposed an optimal control problem on suppressing the CVDs burden. Finally, it is experimentally shown that the CVDs burden can be reduced strategically by making appropriate interventions.

Subject Classification:

• 92B05
• 34D32
• 35B35

Keywords:

• Cardiovascular diseases
• Stability
• Optimal control
• Sensitivity analysis