# A Time-dependent SIR model for COVID-19 with Undetectable Infected Persons

arXiv: https://arxiv.org/abs/2003.00122 · HTML: https://mlsanity.com/paper/2003.00122/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2020.

## Built on by (most cited first, 8 of 8)

- [SIMLR: Machine Learning inside the SIR model for COVID-19 Forecasting](https://mlsanity.com/paper/2106.01590/) (2021)
- [A Simple Explanation for the Phase Transition in Large Language Models with List Decoding](https://mlsanity.com/paper/2303.13112/) (2023)
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- [Modeling time evolving COVID-19 uncertainties with density dependent asymptomatic infections and social reinforcement](https://mlsanity.com/paper/2108.10029/) (2021)
- [Modeling Effect of Lockdowns and Other Effects on India Covid-19 Infections Using SEIR Model and Machine Learning](https://mlsanity.com/paper/2110.03422/) (2021)
- [An Overview of Healthcare Data Analytics With Applications to the COVID-19 Pandemic](https://mlsanity.com/paper/2111.14623/) (2021)
- [Inference and Optimization for Engineering and Physical Systems](https://mlsanity.com/paper/2208.13880/) (2022)
- [Neural Network Augmented Compartmental Pandemic Models](https://mlsanity.com/paper/2212.08481/) (2022)

## Abstract (arXiv)

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 R0 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 R0. For (Q4), we show that herd immunity can be achieved after at least 1-1/R0 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 R0.