Mathematical Modelling of Lifestyle Behaviour and Diabetes Progression Dynamics

This study develops an eight-compartmental deterministic mathematical model to examine how the social adoption of unhealthy lifestyle behaviour influences the progression of diabetes mellitus in a population. Diabetes itself is not transmitted; the transmissible process in the model is the adoption of unhealthy lifestyle behaviour. The model comprises susceptible, unhealthy-lifestyle, healthy-lifestyle, prediabetic, undiagnosed, controlled, complicated and recovered classes. Positivity and boundedness of solutions are established, and the Disease-Free and Endemic Equilibria are obtained. The Basic Reproduction Number, interpreted as a behavioural-adoption threshold, is derived using the Next Generation Matrix, and the local asymptotic stability of the Disease-Free Equilibrium is established by Jacobian analysis when R0 < 1. The numerical parameter values are assumed illustrative values and are not estimates from a specific population. At the baseline parameter set, R0 = 2.833, indicating persistence of unhealthy-lifestyle adoption in the model. Sensitivity analysis identifies β as the strongest positive driver, followed by μ, while γ, α and ρ reduce R0. MATLAB simulations illustrate a larger unhealthy-lifestyle burden at higher adoption rates and a substantial reduction under increased awareness and lifestyle modification. The results are qualitative and theoretical, although it supports prevention, awareness, early diagnosis and sustained healthy-lifestyle promotion as important components of diabetes control but calibration and validation against observed data are needed before they can inform public-health practice.