Browsing by Author "Andima, Robert Nyatundo"

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    Modelling Diabetes and Its Complication in a Resource Constrained Setting
    (Kenyatta University, 2025-10) Andima, Robert Nyatundo
    Diabetes mellitus is a chronic non-communicable disease resulting from the body’s inability to metabolise excess glucose due to impaired insulin secretion or function. It has become a major global burden, with the World Health Organization (WHO) reporting that non-communicable diseases account for 71% of all annual deaths, 85% of which occur in low- and middle-income countries. In this study, the dynamics of diabetes are examined under the influence of strained healthcare resources and patient response behaviour. Two compartmental mathematical models are formulated to describe the transitions between susceptible, diabetic, and hospitalized populations. The first model assumes a constant hospitalization rate, while the second introduces a variable hospitalisation rate that depends on the system’s carrying capacity and per capita hospitalization rate. The basic reproduction number and equilibrium states are derived and analysed to assess disease persistence conditions. Numerical simulations using the explicit Runge-Kutta (4,5) method in MATLAB illustrate the system’s behaviour under varying parameters. The results show that enhancing lifestyle quality among susceptible increases their stability while reducing diabetes prevalence; a higher treatment rate among diabetics raises the hospitalized proportion, whereas increasing the carrying capacity diminishes hospitalization levels.