[Paper Review] Epidemic analysis of COVID-19 in China by dynamical modeling

Liangrong Peng, Wuyue Yang+3 more|arXiv (Cornell University)|Feb 16, 2020

COVID-19 epidemiological studies37 references103 citations

TL;DR

The paper extends SEIR to a generalized SEIR model with a quarantined state and self-protection, estimates key parameters from early Chinese data, and forecasts inflection points, ending times, and total infections across Mainland China, Hubei, and Wuhan.

ABSTRACT

The outbreak of novel coronavirus-caused pneumonia (COVID-19) in Wuhan has attracted worldwide attention. Here, we propose a generalized SEIR model to analyze this epidemic. Based on the public data of National Health Commission of China from Jan. 20th to Feb. 9th, 2020, we reliably estimate key epidemic parameters and make predictions on the inflection point and possible ending time for 5 different regions. According to optimistic estimation, the epidemics in Beijing and Shanghai will end soon within two weeks, while for most part of China, including the majority of cities in Hubei province, the success of anti-epidemic will be no later than the middle of March. The situation in Wuhan is still very severe, at least based on public data until Feb. 15th. We expect it will end up at the beginning of April. Moreover, by inverse inference, we find the outbreak of COVID-19 in Mainland, Hubei province and Wuhan all can be dated back to the end of December 2019, and the doubling time is around two days at the early stage.

Motivation & Objective

• Motivate understanding of COVID-19 dynamics in China during the early outbreak period.
• Develop a generalized SEIR framework that accounts for self-protection and quarantine to analyze epidemic spread.
• Estimate key parameters from official data and use them to forecast inflection points, ending times, and total infections for regions in China.
• Investigate the start date of the outbreak via inverse inference to understand early dynamics.

Proposed method

• Generalize the SEIR model to include seven states: S, P, E, I, Q, R, D.
• Incorporate time-varying cure and mortality rates, and a protection (self-protection) rate that reduces effective contacts.
• Use least-squares regression with simulated annealing to fit unknown parameters and initial conditions to daily quarantined data Q(t).
• Fix latent time gamma^{-1} within a plausible range and explore its impact on other parameters to avoid overfitting.
• Perform sensitivity analysis to assess how β (infection rate) and δ^{-1} (quarantine time) influence final outbreak size and inflection point.
• Apply inverse inference (shooting method) to estimate the outbreak start date from early trajectory.

Experimental results

Research questions

• RQ1 What are the key epidemiological parameters (latent time, quarantine time, protection rate, infection rate) that best describe the early COVID-19 dynamics in China?
• RQ2 How do self-protection measures and quarantine affect the effective reproduction number and the timing of the epidemic inflection point?
• RQ3 Can the model forecast inflection points, ending dates, and total infections for Mainland China, Hubei, and Wuhan, and how do these forecasts compare with observed data?
• RQ4 When did the COVID-19 outbreak likely start in Mainland China, Hubei, and Wuhan according to inverse inference?

Key findings

• The generalized SEIR model with a quarantined state can fit the official quarantined data and capture regional differences in protection and quarantine dynamics.
• Forecasts suggest Beijing and Shanghai would end soon (within two weeks of Feb 16, 2020), and most of Mainland would end by mid-March, with Wuhan ending around early April (based on public data up to Feb 16, 2020).
• Inverse inference indicates the outbreak began 20–25 days before Jan 20, 2020, i.e., around end of December 2019, with an early exponential growth (doubling time ~2 days).
• The infection rate β is near 1, indicating high transmissibility, and the model parameters show longer quarantine times in more developed regions and shorter ones in stricter regions.
• Prediction accuracy improved when accounting for changes in cure and mortality rates over time, reflecting medical and policy responses.
• Beijing and Shanghai’s total infected cases are estimated around 4 hundred, while larger regional totals are forecast for Mainland*, Hubei*, and Wuhan, with regional deviations explained by measures and data reporting changes.