传染病模型SIR的一些研究和应用

Some Research and Applications of the SIR Model for Infectious Diseases

摘要: 传染性疾病历来是人类的公敌，并且传染性疾病具有流行性、季节性和地方性的特点，一些恶性疾病的传播甚至对国家的安全产生严重威胁。因此传染病的防治，成为关系到人类健康和国计民生的重大问题。传染病动力学是对传染病的流行规律进行理论性定量研究的一种重要方法，在这方面数学工作者作了大量的研究工作。传染病的基本数学模型，研究传染病的传播速度、空间范围、传播途径、动力学机理等问题，以指导对传染病的有效的预防和控制。常见的传染病模型按照传染病类型分为SI、SIR、SIRS、SEIR模型等，按照传播机理又分为基于常微分方程、偏微分方程、网络动力学的不同类型。流行病数学是医学数学的一个分支，也是应用数学知识较多的一个分支，为了较准确地描述传染病的模型建立研究进而推广产生了传染病动力学模型，即流行病数学模型。随着对传染病的模型研究的深入，人们发现其所涉及的问题涵盖了医学和生物学等众多学科，因此具有很强的应用背景和实际意义。而本文主要研究的是传染病SIR模型，将SIR模型运用到2020年武汉新型冠状病毒导致的疫情当中，对疫情进行数值模拟和预测，分析疫情的发展趋势和提供一些防疫抗疫上的帮助。

Abstract: Infectious diseases have always been the common enemy of humanity. They are characterized by their epidemic nature, seasonality and locality. The spread of some malignant diseases even poses a serious threat to national security. Therefore, the prevention and control of infectious diseases have become a major issue related to human health, national economy and people’s livelihood. Infectious disease dynamics is an important method to theoretically and quantitatively study the epidemic law of infectious diseases. Mathematicians have done a lot of research work in this area. The basic mathematical model of infectious diseases, to study the transmission speed, spatial range, transmission route, dynamic mechanism and other issues of infectious diseases, so as to guide the effective prevention and control of infectious diseases. This paper mainly studies the SIR Model for infectious diseases. It applies the SIR Model to the epidemic caused by the novel coronavirus in Wuhan in 2020, conducts numerical simulation and prediction of the epidemic, analyzes the development trend of the epidemic and provides some assistance in epidemic prevention and control.