本文主要基于经典传染病仓室模型，运用参数估计、下一代矩阵的求解 方法，推导基本再生数，研究首要干预政策“疫苗接种”对传播的影响，并 进行数值模拟。

首先，本文基于 SIR,SIRS,SEIR,SEITR 四种经典仓室模型，研究了常见的 参数估计参数，针对实际数据样本研究，对比总结了关于世代间隔、潜伏期 等关键参数的参数估计结果，作为后文的数值模拟的依据，并讨论不同传播 特征对应的模型。

本文进一步采用下一代矩阵方法，求解传染病的传播模型，分别解出单 仓室的 SIR、多仓室的 SEIR 模型下的基本再生参数 R₀，并对 SEIR 模型加入 疫苗干预，研究有效再生参数 R_t。

此后进行了数值模拟，仿真无疫苗干预情况和疫苗干预情况下的传染病 传播情况，选择感染率和疫情消亡时间等数据为指标，量化评估防控效果。

最后，基于实际数据，人口密度、感染状态等其他因素也会通过影响参 数影响模型传播。因此，将参数建立为这些子变量的函数，进行灵敏度分析， 讨论模型参数的变化对模型稳定性的影响，为有效阻断传染病传播提供参考。

This paper studys and derives classical infectious disease models, parameter estimation, next-generation matrix solution methods, derivation of basic regeneration numbers, and the impact of vaccination on transmission.

First, four models are derived and developed, and the common parameter estimation methods are studied. The results of parameter estimation of key parameters such as generation interval are compared and summarized, which are used as the basis for the numerical simulation in the later paper, and the models corresponding to different transmission characteristics are discussed.

Then the next-generation matrix approach is adopted to solve the transmission model and the basic regeneration parameters R₀ under the SIR of single-compartment and SEIR of multi-compartment models respectively, and vaccine intervention is added to the SEIR model to study the effective regeneration parameter R_t.

Thereafter, numerical simulations were conducted to simulate the spread of infectious diseases under natural and vaccine intervention scenarios, and the infection rate and epidemic extinction time were selected as indicators to discuss the prevention and control effects.

Finally, based on realistic data, other factors such as population density can also affect the model spread by influencing the parameters. Therefore, the parameters are established as a function of these sub variables, sensitivity analysis is performed, and the effect of changes in model parameters on model stability is discussed to provide a reference for effectively interrupting the spread of infectious diseases.