Browsing by Author "Subawickrama, H. D. K. M."

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    Mathematical modeling of diabetes mellitus
    (Faculty of Science, University of Kelaniya Sri Lanka, 2024) Subawickrama, H. D. K. M.; Munasinghe, J.; De Silva, T. M. M.
    Diabetes is becoming a silent epidemic that is endangering public health worldwide. For instance, the majority of the 422 million diabetics globally reside in low- and middle-income nations, and the illness directly causes 1.5 million fatalities per year. In recent decades, the prevalence and complexity of the chronic medical condition diabetes have raised serious concerns about global health. As a result, studying and developing mathematical models becomes increasingly important since they provide an advanced perspective for realizing the complex nature of the disease and creating realistic care with preventive measures. Furthermore, it is a useful tool for tracking the rising incidence of the disease and creating affordable control measures for both its incidence and consequences. Thus, the main focus of this study is to propose a mathematical model that is employed to forecast changes in the prevalence of diabetes using a saturated incidence rate, which reflects a diminishing rate of new infections as the number of affected individuals increases, by extending the Diabetes Complication (DC) and Susceptible Diabetes Complication (SDC) models. It has been established which factors lead to both endemic and disease-free equilibriums. The conditions that contribute to the equilibrium between endemic and disease-free states are identified. Based on the eigenvalues of the Jacobian matrix, the local stability of the equilibrium points has been determined. Since diabetes is not a transmissible disease, there is no disease-free equilibrium and when the constant term 𝑅0 < 1, the endemic equilibrium point is locally asymptotically stable. Additionally, the Lyapunov function theory has been utilized to study global stability. We observe the effect of the term saturated incidence rate under some parameter conditions. Based on data gathered from annual mortality reports and health bulletins that have been published by the Ministry of Health, Sri Lanka and the United Nations’ World Population Prospects the parameters for complications related mortality rate, the natural mortality rate, and the birth rate are estimated. Numerical simulations using MATLAB’s ODE 45 technique are conducted to validate the analytical findings of the proposed model and assess its approach. This model also monitors the number of susceptible people as well as the population with and without diabetes complications. We predict that the 2.29 million will be the approximate Sri Lankan total prevalence of diabetes in 2024 and additionally, it notes an average annual increase of about 0.2199% in diabetes prevalence. The model’s accuracy is highlighted by its minimal average relative error, making it effective for forecasting and valuable for informing disease management strategies.