Qualitative analysis and stability of a mathematical model for the spread of obesity

Obesity is the excessive accumulation of fat mass that negatively affects quality of life at multiple levels: health (physical and mental), society, economy, etc. It is a dangerous epidemic that affects developed and developing countries alike. In this article, we propose a continuous-time dynamic epidemiological model that describes the transmission of obesity within an infected population. By using the Routh-Hurwitz criteria and constructing Lyapunov functions, we obtain the local and global stability of the equilibrium both in the presence and absence of disease. We perform a sensitivity analysis to determine the contribution and impact of each model parameter on the basic reproduction number R₀ . Finally, the theoretical results are illustrated by numerical simulation via Matlab.