Stability and Prediction of HFMD Dynamics in Malaysia using an SIR Model

Abstract

Hand, foot, and mouth disease (HFMD) remains a significant public health concern in Asia, with Malaysia and neighbouring countries frequently reporting outbreaks. To better understand its transmission dynamics, this paper applies a Susceptible-Infected-Recovered (SIR) model to HFMD in Malaysia. The analysis focuses on model positivity, equilibrium behaviour, and stability, while the basic reproduction number (R₀) is derived using the next-generation method. Two threshold scenarios are considered: when R₀<1, the disease-free equilibrium is stable, indicating eventual eradication, whereas when R₀>1, the endemic equilibrium is stable, signifying sustained transmission. Numerical simulations support these theoretical results and emphasize the critical role of R₀ in shaping outbreak outcomes. A key contribution of this paper is the examination of infection risk variation, showing that higher risks accelerate the shift to endemic persistence, while lower risks extend the stability of the disease-free state. Overall, the findings highlight the importance of threshold dynamics and infection risk in determining HFMD spread. By integrating analytical and numerical approaches, this study offers insights that can inform more effective public health strategies in Malaysia.