Regional and seasonal analysis of influenza epidemics: A mathematical modeling study of 15 provinces in China

Influenza, an acute infectious disease of the respiratory system caused by the influenza virus, is marked by its multiple subtypes, high contagion rates and seasonal epidemic outbreaks. In China, influenza exhibits a significant seasonal distribution pattern primarily influenced by climatic and geographic factors. In this paper, we formulate a non-autonomous periodic SEIR model, considering the transmission rate as a time-varying parameter to more accurately depict the seasonal variations of influenza. The model derives the basic reproduction number and establishes the global asymptotic stability for the disease-free equilibrium. The study further demonstrates the existence of periodic solutions along with the uniform persistence of the model. Using the DRAM–MCMC algorithm and influenza data from 15 provincial areas in China, the best-fit parameter values are identified, allowing for the estimation of the average basic reproduction number based on these fitted parameters. The study reveals geographical and seasonal variations in influenza, highlighting pronounced seasonality in specific provinces and atypical summer peaks. Ningxia Hui autonomous region shows high basic reproduction numbers, indicating a strong potential for influenza transmission. In provinces such as Gansu and Anhui, the time-averaged basic reproduction number consistently overestimates the actual basic reproduction number, whereas in regions such as Guangdong and Zhejiang it underestimates transmission potential. Variations in transmission rates between coastal and inland regions, incubation periods and recovery times affect epidemic spread, necessitating tailored prevention and control strategies. Long-term data analysis identifies trends and underlying causes of abnormal influenza fluctuations, offering forward-looking guidance for public health policy.