Epidemiology simulation: numerical techniques for analyzing type 2 diabetes model and its prevention measures

Abstract

Type 2 diabetes (T2D) is a chronic illness that affects how well the body uses glucose, an essential energy source. Individuals with type 2 diabetes do not produce enough insulin or do not respond to control blood sugar levels. Clinical trials have suggested that poor nutritional habits may contribute to an increase in the incidence of type 2 diabetes. We investigated the dynamics of type 2 diabetes mellitus (T2D), which was formulated based on an epidemic mathematical model. The model categorizes the population into five compartments: Susceptible S(t), Affected A(t), Treated T(t), Healthy Lifestyle L(t), and Prevented P(t) individuals. We used the Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) to provide a thorough analytical study of this distinct model. To confirm the region of convergence in the HAM solutions for our model, the h-curves are provided. MATLAB coding was used for comparison with HAM and HPM to verify the accuracy and efficacy of the obtained solutions. We noticed no substantial difference between the analytical and numerical results. Moreover, in order to examine the behavior of the model individuals, we varied each parameter. Through this analysis, we obtained valuable insights into the responses of the type 2 diabetes model under various conditions and scenarios. This research offers valuable insights into the utilization of semi-analytical methods for analyzing epidemiological models related to infectious diseases, providing significant utility for researchers in the field.