In this paper, we applied the Sobol’s method on an already existing mathematical model of coronavirus disease 2019 (covid-19). The objectives of this research work are to study the individual effects of involved parameters as well as combine (mutual) effects of parameters on output variables of covid-19 model. The study is also useful to identify the ranking of key model parameters and factors fixing. The ultimate goal is to identify the controlling parameters, which eventually will help decision makers to explore various policy options to control the covid-19 pandemic. For this purpose, first we present the model with its basic properties that are positivity and existence of solution. Then use the Sobol’s method to discuss the individual effects of involved parameters as well as combine (mutual) effects of parameters on output variables of covid-19 model. Finally, we present the results, discussions and concluding remarks about key model parameters and identifying the controlling parameters, which eventually will help decision makers to explore various policy options to control the covid-19 pandemic.

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The basic theme of this work is to identify the optimal measurement locations for pressure and flow in the systemic circulation to detect aortic stenoses and aneurysms in early stages of a disease. For this purpose, a linear elastic lumped parameter model of the fluid dynamical simulator, major arterial cardiovascular simulator (MACSim), is considered and global sensitivity analysis is applied to identify the better measurement locations for pressure and flow in the systemic circulation. The obtained results of sensitivity analysis provide insight that enable the experimentalists to optimize their experimental setups for detecting aortic stenoses and aneurysms using parameter estimation process. From the results, it is observed that the stenosis in the thoracic aorta can be identified from both pressure and flow at the location itself, nearby nodes, aorta ascendens, arcus aorta, arteria subclavia and arteria axillaris. On the other hand, the preferable measurement locations for abdominal aneurysms are locations themselves, nearby nodes and left/right leg of the body.

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In this paper, a multi-compartment 0D model of the blood flow is considered to study the vessel abnormalities (stenoses and aneurysms) in the human systemic circulation (SC). In the complete SC, different levels of stenosis and aneurysms are artificially created by decreasing and increasing the vessel diameters respectively and their effects on pressure and flow are studied using sensitivity analysis (SA). Normalized local sensitivity analysis (LSA) is used to study the impact of stenosis and aneurysms on pressure and flow wave pattern. Furthermore, global sensitivity analysis (GSA), Sobol’s method is used to quantify the overall influence of stenoses and aneurysms in the complete SC. The results of global sensitivity analysis revealed that the impact of both stenoses and aneurysms is strong within the individual structures (arm, legs, carotid bifurcation, aorta), while, aortic stenoses and aneurysms have effect on almost all downstream nodes. Moreover, the study could be useful for medical doctors, teachers and students to observe the hemodynamical changes in the SC with respect to vessel abnormalities, which could further help in making any clinical decision for patients having different levels of vessel abnormalities in any part or structure of the SC.