<p>Measles is a severe infectious respiratory disease that predominantly affects children and is largely preventable by vaccination. Despite the availability of a vaccine, measles continues to pose a significant threat to global health management. The disease is the primary cause of illness and death in children under five years of age. The majority of measles-related fatalities occur in countries with inadequate health infrastructure and low per capita income. In this study, a fractional order mathematical model is constructed for the population of individuals infected with measles, divided into three compartments: the number of susceptible individuals (<i>S</i>), the number of infected individuals (<i>I</i>), the number of vaccinated and recovered individuals (<i>V</i>). The Caputo derivative definition was employed as the fractional derivative. The stability analysis of the fractional model for measles was conducted, and numerical solutions were obtained through the utilisation of the Euler method. Consequently, the dynamics of the number of individuals with measles disease in a population were created and interpreted.</p>