Caputo Fractional-Order Model of Measles and Reye’s Syndrome: Insights from Uk Surveillance Data on Stability and Bifurcation

Abstract

This paper proposes a fractional-order compartmental S-V-I-R-M model to investigate the transmission dynamics of measles and the potential occurrence of Reye's syndrome associated with aspirin use during infection. The model is formulated using the Caputo fractional derivative in order to incorporate memory and hereditary effects that are not captured by classical integer-order models, thereby providing a more realistic representation of epidemic dynamics. Fundamental qualitative properties of the model, including existence, uniqueness, positivity, and boundedness of solutions are rigorously established. The basic reproduction number is derived, and all equilibrium points are identified. A local stability analysis of the disease-free and endemic equilibria is performed by means of fractional-order stability theory. Furthermore, a detailed bifurcation analysis is conducted, revealing the presence of both forward and backward bifurcations. The results demonstrate that the fractional order significantly influences stability thresholds and the bifurcation behavior, thereby altering disease persistence conditions. Model parameters are estimated using measles incidence data and vaccination coverage reported by the UK Health Security Agency for the period 2019-2023 based on a 21-month observational dataset. Numerical simulations are carried out to assess the impact of public health interventions, including increased vaccination coverage and reduced aspirin use among infected individuals. The results demonstrate that the combined intervention strategy is more effective than either intervention used separately in suppressing disease transmission and reducing sustained outbreaks.