In this paper, a class of fractional deterministic and stochastic susceptible-infected-removed- susceptible (SIRS) epidemic models with vaccination is proposed. For the fractional deterministic SIRS epidemic model, the existence of solution and the stability of equilibrium points are analyzed by using dynamic method. Then, the appropriate controls are established to effectively control the disease and eliminate it. On this basis, the fractional stochastic SIRS epidemic model with vaccination is further considered, and a numerical approximation method is proposed. The correctness of the conclusion is verified by numerical simulation.

The number of new human brucellosis cases has shown a periodic upward trend in Changji city, Xinjiang. It is essential to estimate the transmission intensity of brucellosis and put forward effective prevention and control measures. According to the mechanistic characteristics of brucellosis transmission, we established a seasonal dynamic model to describe the transmission of brucellosis among sheep/cattle, environment and humans. The constructed seasonal dynamic model SEIVW with periodic transmission rates has perfectly simulated the periodic upward trend of new human brucellosis cases in Changji city from 2020 to 2023. The mean absolute percentage error (MAPE) between the model-predicted and actual values was 33.20% for new cases and 10.56% for cumulative new cases. Long-term prediction over the next 25 years suggested that the number of new human brucellosis cases will first show an upward trend, reaching a peak of 3688 cases in July 2032, followed by a gradual decline and stabilization after 2038. Furthermore, we estimated the basic reproduction number R₀ for brucellosis transmission is 2.8228 (95% CI: 2.8161-2.8295), indicating that the disease transmission remains severe and persistent. Parameter sensitivity analysis quantitatively identified key intervention strategies: increasing the culling rate of infected sheep/cattle, and improving the vaccination rate of susceptible sheep/cattle are the primary control measures. Additionally, enhancing environmental disinfection frequency can be served as a supplementary measures.