A Time-Dependent SIR Model for COVID-19 With Undetectable Infected Persons
| Autor: | Tzu-Hsuan Liu, Cheng-Shang Chang, Yi-Cheng Chen, Ping-En Lu |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Coronavirus disease 2019 (COVID-19) Spectral radius Computer Networks and Communications Machine Learning (stat.ML) law.invention Machine Learning (cs.LG) 03 medical and health sciences Matrix (mathematics) 0302 clinical medicine law Statistics - Machine Learning Statistics 030212 general & internal medicine Quantitative Biology - Populations and Evolution 030304 developmental biology Random graph 0303 health sciences Diagram Populations and Evolution (q-bio.PE) Outbreak Computer Science Applications Transmission (mechanics) Control and Systems Engineering FOS: Biological sciences Epidemic model |
| Zdroj: | IEEE Transactions on Network Science and Engineering |
| ISSN: | 2327-4697 2334-329X |
| DOI: | 10.1109/tnse.2020.3024723 |
| Popis: | In this paper, we conduct mathematical and numerical analyses to address the following crucial questions for COVID-19: (Q1) Is it possible to contain COVID-19? (Q2) When will be the peak and the end of the epidemic? (Q3) How do the asymptomatic infections affect the spread of disease? (Q4) What is the ratio of the population that needs to be infected to achieve herd immunity? (Q5) How effective are the social distancing approaches? (Q6) What is the ratio of the population infected in the long run? For (Q1) and (Q2), we propose a time-dependent susceptible-infected-recovered (SIR) model that tracks 2 time series: (i) the transmission rate at time t and (ii) the recovering rate at time t. Such an approach is more adaptive than traditional static SIR models and more robust than direct estimation methods. Using the data provided by China, we show that the one-day prediction errors for the numbers of confirmed cases are almost in 3%, and the total number of confirmed cases is precisely predicted. Also, the turning point, defined as the day that the transmission rate is less than the recovering rate can be accurately predicted. After that day, the basic reproduction number $R_0$ is less than 1. For (Q3), we extend our SIR model by considering 2 types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak in such a model is characterized by the spectral radius of a 2 by 2 matrix that is closely related to $R_0$. For (Q4), we show that herd immunity can be achieved after at least 1-1/$R_0$ fraction of individuals being infected. For (Q5) and (Q6), we analyze the independent cascade (IC) model for disease propagation in a configuration random graph. By relating the propagation probabilities in the IC model to the transmission rates and recovering rates in the SIR model, we show 2 approaches of social distancing that can lead to a reduction of $R_0$. Comment: 18 pages, 12 figures, 2 table, Parts of the codes used in this paper will be placed on GitHub (https://github.com/PingEnLu/Time-dependent_SIR_COVID-19), The latest version will be placed on http://gibbs1.ee.nthu.edu.tw/A_TIME_DEPENDENT_SIR_MODEL_FOR_COVID_19.PDF |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|