A Time-Dependent SIR Model for COVID-19 With Undetectable Infected Persons

• Published in: IEEE transactions on network science and engineering Vol. 7; no. 4; pp. 3279 - 3294
• Main Authors: Chen, Yi-Cheng, Lu, Ping-En, Chang, Cheng-Shang, Liu, Tzu-Hsuan
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.10.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Coronavirus; Coronaviruses; COVID-19; Disease control; Disease transmission; Diseases; Epidemics; Government; herd immunity; Impact analysis; independent cascade; Mathematical analysis; Mathematical model; Matrix methods; Numerical models; Outbreaks; Phase transitions; Predictive models; SARS-CoV-2; Social distancing; Sociology; Statistics; superspreader; Time dependence; time-dependent SIR model; undetectable infection; Viral diseases; China; COVID-19; herd immunity; undetectable infection; SARS-CoV-2; independent cascade; time-dependent SIR model; Coronavirus; social distancing; superspreader
• ISSN: 2327-4697; 2334-329X
• DOI: 10.1109/TNSE.2020.3024723

In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time t. Using the data provided by China authority, we show our one-day prediction errors are almost less than 3%. The turning point and the total number of confirmed cases in China are predicted under our model. To analyze the impact of the undetectable infections on the spread of disease, we extend our model by considering two types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak is characterized by the spectral radius of a 2 X 2 matrix. If R 0 > 1, then the spectral radius of that matrix is greater than 1, and there is an outbreak. We plot the phase transition diagram of an outbreak and show that there are several countries on the verge of COVID-19 outbreaks on Mar. 2, 2020. To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network. We show two approaches of social distancing that can lead to a reduction of the effective reproduction number R e .