一类具有疫苗影响的流感模型研究及统计分析

Research and Statistical Analysis of a Type of Influenza Model with Vaccine Influence

摘要: 针对一类改进的SVEIR流感传播动力学模型，探讨了参数估计与拟合方法，并分析了疫苗接种对流感传播的影响。首先，假设现有确诊病例数遵循泊松分布，通过Bootstrap方法生成时间序列样本，采用马尔可夫链蒙特卡洛(MCMC)算法实现后验分布的高效采样对模型参数进行估计。随后，为验证模型的有效性，利用实际流感数据进行检验，结果表明模型能够较好地捕捉流感的传播动态。进一步，通过敏感性分析，评估了疫苗接种率$v$ 对基本再生数${\Re }_0$ 和最终感染规模的影响。研究发现，提高疫苗接种率可显著降低流感的传播风险。

Abstract: For a class of improved SVEIR influenza transmission dynamics model, parameter estimation and fitting methods are discussed, and the impact of vaccination on influenza transmission is analyzed. First, assuming that the number of confirmed cases follows a Poisson distribution, the Bootstrap method is used to generate time series samples, and the Markov Chain Monte Carlo (MCMC) algorithm is used to achieve efficient sampling of the posterior distribution to estimate the model parameters. Subsequently, in order to verify the effectiveness of the model, actual influenza data were used for testing, and the results showed that the model can better capture the transmission dynamics of influenza. Furthermore, through sensitivity analysis, the impact of vaccination rate $v$ on the basic reproduction number ${\Re }_0$ and the final infection scale was evaluated. The study found that increasing the vaccination rate can significantly reduce the risk of influenza transmission.