Measles transmission dynamics and optimal control in Guangdong, China

This study focuses on the cyclical epidemic characteristics of measles in Guangdong Province and constructs a non-autonomous SVEIR model that integrates seasonal transmission and vaccination dynamics, with a particular emphasis on analyzing the immune protection mechanisms of high-risk populations aged 0–24 months. This model introduces a time-varying propagation rate (Fourier function fitted to weekly data, [Formula: see text]), time-varying vaccination rate and vaccine protection rate, and optimizing vaccination strategies through optimal control theory. Mathematical analysis confirms that the basic reproduction number [Formula: see text] represents the key threshold determining the persistence or extinction of measles, with estimated value as 0.87 (95% CI: 0.43–1.3). Numerical simulations indicate that sustaining a vaccination rate ([Formula: see text]99%) can suppress the annual incidence rate below 1/100,000. However, reducing the rate to 98.5% would trigger a sharp surge in cases within three years, with the incidence rate projected to reach 0.9‰ by 2030. Furthermore, vaccination efforts averted an estimated 80 million infections between 2005 and 2021. Optimization strategies indicate that prioritizing vaccination for the 0–2 age group can shorten the epidemic cycle by 30%, and real-time monitoring combined with vaccination coverage of [Formula: see text]99% can achieve herd immunity.