Eigenvalue Elasticity Analysis of Mathematical Model of Dynamics of Diabetes and its Complications in a Population

In this paper, a mathematical model of dynamics of diabetes and its complications was presented to explore the parameters with the greatest impact on the model. The model allows for the individuals to move from the susceptible class to the treated class. The model exhibit one equilibrum state, namely, the disease prevalent equilibrium state. The local and global asymptotic stability of the equilibrium state was determined using quadratic Lyapunov method. Eigenvalue elasticity analysis of the model parameters was carried out and parameter d (mortality rate due to complications) has the highest positive eigenvalue elasticity value. Also, using the eigenvalue sensitivity analysis, the parameter d has the highest positive value. The analysis revealed that parameter d has the greatest impact on the formulated mathematical model of disease dynamics which must be put into consideration by the health care policy makers in order to reduce the rate of mortality due to the disease.