A general model of non-communicable diseases and its qualitative analysis without finding the eigenvalues

Abstract

Obtaining the analytical solutions of a linear ordinary differential equations is impossible without finding the eigenvalues. In this study, a general linear model of non-communicable disease (NCD) is formulated using the compartmental analysis and its qualitative properties are analyzed without finding the eigenvalues. NCDs are diseases which are not passed from person to person. The proof of the qualitative properties of the general model including the existence and uniqueness of its solution and equilibrium, and the positivity and boundedness of its solutions are provided. The global stability of the general model is analyzed using the theorem of compartmental matrix and Lyapunov function. It is found that the model has one unique non-negative equilibrium which is globally exponentially stable. As a real-world example, the general model and its qualitative analysis are implemented to a NCD, namely venous thromboembolism (VTE) among pregnant and postpartum women. VTE is selected in this study as it is a major global health burden due to its association with disability and lower quality of life and death.