基于SALIR模型的病毒传播研究——以COVID-19为例

Study on the Spread of the Virus Based on SALIR Model —A Case Study on COVID-19

摘要: 传染病毒的传播是人类健康问题非常重大的挑战，如2003年的SARS、2020年的新冠肺炎等病毒的传播给全世界造成了严重的伤害，因此研究病毒的传播是当今非常重要的科学问题之一。本文根据病毒传播的特性构建了基于常微分方程的SALIR模型，模型中重点考虑新冠肺炎病毒传播中无症状感染者的影响。通过对模型进行数值模拟和分析，发现模型能较好地反映被感染人数增长的一般规律，与真实数据基本相符。同时，我们还考虑了病毒传播能力对总感染人数的影响，发现病毒传播能力较弱时，不会造成大面积的感染，而当传染能力超过一定的阈值，病毒就会大面积的爆发。

Abstract: The spread of infectious viruses poses a severe threat to human health. Viruses such as SARS in 2003 and COVID-19 in 2020 have caused serious damage around the world. Therefore, carrying out studies on the spread of viruses is one of the most meaningful scientific researches today. According to the properties of virus, SALIR Model based on ODE (ordinary differential equation) was con-structed. The model focuses on the impact of asymptomatic infections in the spread of COVID-19 vi-ruses. Through numerical modeling and analysis of the model, we found that the model can reflect the general rule of the increase in the number of infected people, which is basically consistent with the truthful data. Moreover, we also considered the impact of virus transmission capacity on the to-tal number of infected people and found that when the virus is found to be weak in transmission, it will not cause widespread infection. However, when the intensity of the infection exceeds a certain threshold, it will bring the massive outbreak of virus.