SIR模型，是研究传染病传播过程最经典、最基本的动力学模型，本文前半节学习了不同驱动情况下的SIR模型，后半节则在此基础上研究了新冠肺炎在新加坡的发展状况。

前半部分主要学习了对接触规则、感染规则、感染之后个体水平上疾病的发展情况这三方面作出规定后，经典SIR模型在不同驱动下的不同情况。内容上，具体从感染驱动者（易感者/感染者）以及感染时间（接触周期开始/结束）两个维度建立模型进行研究；方法上，利用有关流体力学奇异极限问题的理论分析和数值模拟两种手段，得出结论。

从理论分析的角度看，驱动者不同，感染时间不同，建立的模型完全不同；从数值模拟结果直观看出，在特殊情况下，结束时感染的模型解可收敛于开始时感染的模型解。

后半部分对经典模型进行改进，使其适用于本次新冠肺炎的疫情研究，并将其应用于新加坡疫情的研究。创新之处主要在于将感染者分为三类：无症状感染者、报告的确诊患者、未报告的有症状患者，这是符合实际情况的。

The susceptible-infectious-recovered (SIR) model is the most classical and basic dynamic model. In the first part, different SIR models under different driving conditions are studied. In the second part, COVID-19 epidemic in Singapore is the key point.

Firstly, based on the classical SIR model, the improved model is learned in this article, after regulating the contact rules, infection rules and the development of diseases when one gets infected. In terms of the content, the model is established from two dimensions including drivers of infection (susceptible or infected individuals) and time of infection (at the start or end of the contact). Considering the method, one is the theoretical analysis in the singular limit problem of fluid mechanics, and the other is numerical simulation.

 On the part of theoretical analysis, different models correspond to different drivers of inflection and infection time. As for the results of numerical simulation, it is obvious that in special cases, the solution of an infection model in the end of the contact would converge to the solution at the beginning.

Secondly, the classical model is modified to be suitable for the outbreak of COVID-19 in Singapore. It is innovative to divide the infected into three categories: asymptomatic, reported confirmed, and unreported symptomatic one, which is reasonable.

In conclusion, if the transmission rate is constant, the turning point is around May 24 in Singapore, and finally there might be 10.78 thousand people being inflected. And we will continue to study the new situation of the epidemic in the future.