Developing An Epidemiological Mathematical Model For Type 2 Diabetes Mellitus In Zamfara State, Integrating Lifestyle And Treatment Factors

This research presents a mathematical model comprising a system of ordinary differential equations (ODEs) to investigate the dynamics of a population concerning diabetes and its complications.The model considers the recruitment rate of successive individuals, progression rates between different health states, and the impact of lifestyle factors on disease incidence.The analysis focuses on the existence and uniqueness of solutions within a biologically feasible region.The results demonstrate the existence of an invariant region , where the model is mathematically well-posed, ensuring the positivity of population variables.Furthermore, theorems on the existence and uniqueness of solutions are established, affirming the stability of the model under Lipschitz conditions.The study explores the region of interest for the model parameters and establishes the existence of a unique solution within specified bounds.The disease-free equilibrium is investigated, revealing a stable equilibrium point denoted as , representing a population with diabetes-free individuals.Overall, the research provides a comprehensive analysis of the proposed mathematical model, offering understandings into the dynamics of diabetes and its complications within a population context.