Mathematical Modelling and Stability Analysis for Diabetes Predicting System

摘要

In this paper, a model consisting of four states of diabetics is proposed for predicting the development of diabetes. Suppose that all diabetics in the model are with type 2 diabetes and that there is no input or output. While the states of diabetics can alter between each other. Under these assumptions, a model of partial differential equations is derived. The general well-posedness result of the system is obtained and the exponential stability of dynamic solution converging to the steady-state solution is proved. Herein, the steady-state solution gives the stable distribution probability of diabetics (the predicted result). Furthermore, some reliability indices are discussed. The results of some numerical simulations for the cost problem are illustrated to conclude that, if diabetics want to live a higher standard and cost less, they need to follow doctor's advice, learn more knowledge about diabetes, pay attention to their diet and so on which can make the recovery rate larger.