[Paper Review] A time series method to analyze incidence pattern and estimate reproduction number of COVID-19

Soudeep Deb, Manidipa Majumdar|arXiv (Cornell University)|Mar 24, 2020

COVID-19 epidemiological studies14 references49 citations

TL;DR

The paper develops a time-series ARIMA-based model with time-dependent quadratic trend to analyze COVID-19 incidence patterns, assess lockdown effects, and estimate country/province-level reproduction numbers (R0) using serial interval distributions.

ABSTRACT

The ongoing pandemic of Coronavirus disease (COVID-19) emerged in Wuhan, China in the end of 2019. It has already affected more than 300,000 people, with the number of deaths nearing 13000 across the world. As it has been posing a huge threat to global public health, it is of utmost importance to identify the rate at which the disease is spreading. In this study, we propose a time series model to analyze the trend pattern of the incidence of COVID-19 outbreak. We also incorporate information on total or partial lockdown, wherever available, into the model. The model is concise in structure, and using appropriate diagnostic measures, we showed that a time-dependent quadratic trend successfully captures the incidence pattern of the disease. We also estimate the basic reproduction number across different countries, and find that it is consistent except for the United States of America. The above statistical analysis is able to shed light on understanding the trends of the outbreak, and gives insight on what epidemiological stage a region is in. This has the potential to help in prompting policies to address COVID-19 pandemic in different countries.

Motivation & Objective

• Identify the incidence growth patterns of COVID-19 across regions using time-series analysis.
• Incorporate lockdown effects into the incidence model to assess policy impact.
• Estimate basic reproduction numbers (R0) for different countries using serial interval distributions.
• Determine change-points in incidence trends and interpret epidemiological stages.
• Validate model diagnostics and predictive performance across regions.

Proposed method

• Model log-incidence as log(theta_t) = f(t, tau) + gamma L_t + u_t with f(t, tau) as a time-dependent quadratic trend.
• Allow trend coefficients to change at an estimated change-point eta, giving beta_{m,t} piecewise (before/after eta).
• Assume ARMA structure for the error term and select p, q, and eta via AIC.
• Incorporate lockdown indicator L_t as a covariate in the mean function to assess policy impact.
• Estimate R0 for each country using maximum likelihood with several candidate gamma-distributed serial intervals (SARS-like, MERS-like, and average).
• Perform residual diagnostics (Box-Ljung, QQ, PACF) and forecast evaluation (RMSE) using rolling training windows.

Experimental results

Research questions

• RQ1 What is the time trend pattern of daily incidence across Chinese provinces and six countries?
• RQ2 How does lockdown affect the incidence trajectory after accounting for underlying trends?
• RQ3 What are the estimated change-points in incidence trends, and how do these differ by region?
• RQ4 What are the country- and province-level estimates of the basic reproduction number R0 under different serial interval assumptions?
• RQ5 How robust are the model diagnostics and predictive performance across regions?

Key findings

• A time-dependent quadratic trend best captures the incidence pattern across regions, with change-points differing by region.
• Lockdown effects are significant in some provinces/countries, while not in others, suggesting timing and context influence policy impact.
• Most Chinese provinces show a decreasing growth pattern after their estimated change-point, whereas several other countries show continued growth through the study period.
• Estimated R0 values for China, India, Iran, Italy, South Korea, and the US largely align with existing WHO ranges for several serial interval assumptions, though the US estimates are notably higher under some distributions.
• Box-Ljung tests indicate residuals are non-autocorrelated for all countries, and RMSE for three-day-ahead predictions remains acceptable in many provinces but varies by country.