Modelling Diabetes and Its Complication in a Resource Constrained Setting
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Date
2025-10
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Kenyatta University
Abstract
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.
Description
A Research Submitted in Partial Fulfilment of the Requirements for the Award of the Degree of Doctor of Philosophy (Applied Mathematics) in the School of Pure
and Applied Sciences of Kenyatta University. October 2025
Supervisors
Winifred N. Mutuku
Farai Nyabadza
Kennedy Awuor