Dynamic analysis of a diabetes mathematical model including heredity parameter and multiple time delays

Diabetes, a serious health issue, is currently regarded as an epidemic (Tabish in J Health Sci 1(2):5–8, 2007). In this study, delayed differential equations have been employed to construct a diabetic population model with two time delays. The population has been divided into three categories: non-diabetic, prediabetic, and diabetic. The first delay parameter reflects the time it takes for individuals with prediabetes to progress from the prediabetic class to the diabetic class. The second delay parameter describes how long it takes for diabetes to develop because of inheritance. The existence and uniqueness of a positive equilibrium point of the model have been established. Pertaining to the time delays, the local and global stability of the equilibrium point of the model have been examined. For the purpose of establishing Hopf bifurcation, four time delay possibilities were considered: a system with no time delay, a system with either time delay, and a system with both time delays. Numerical simulations have been performed to validate the analytical results. It is crucial to incorporate time delays into the mathematical model of diabetes in order to better encompass the dynamics of diabetes, as evidenced by the existence of stability switches in relation to time delays. The model’s applicability has been demonstrated by calibrating model parameters for the data of the diabetic population in India for the years 2009–2019 using genetic algorithm. According to global sensitivity analysis, the number of people with diabetes can be reduced with the help of preventative and control strategies like stress management, exercise, and a nutritious diet.