[Paper Review] The Data Forecast in COVID-19 Model with Applications to US, South Korea, Brazil, India, Russia and Italy

Bo-Cyuan Lin, Yen-Jia Chen+4 more|arXiv (Cornell University)|Nov 5, 2020

COVID-19 epidemiological studies9 references4 citations

TL;DR

This paper proposes and applies two modified epidemic models—SIARD and SQIARD—incorporating asymptomatic infections and quarantine dynamics to forecast COVID-19 trends in the US, South Korea, Brazil, India, Russia, and Italy. Using real infection data and parameter calibration via discrete-time difference equations, the SQIARD model, which includes quarantine screening data, shows improved forecast accuracy over SIARD, particularly in the US, with a 9-day effective prediction interval at 5% error compared to 6 days for SIARD.

ABSTRACT

In this paper, we firstly propose SQIARD and SIARD models to investigate the transmission of COVID-19 with quarantine, infected and asymptomatic infected, and discuss the relation between the respective basic reproduction number $R_0, R_Q$ and the stability of the equilibrium points of model. Secondly, after training the related data parameters, in our numerical simulations, we respectively conduct the forecast of the data of US, South Korea, Brazil, India, Russia and Italy, and the effect of prediction of the epidemic situation in each country. Furthermore, we apply US data to compare SQIARD with SIARD, and display the effects of predictions.

Motivation & Objective

• To develop and calibrate mathematical models that account for asymptomatic infections and quarantine measures in forecasting COVID-19 spread.
• To compare the predictive performance of the SIARD model (without quarantine) and SQIARD model (with quarantine) using real-world data.
• To estimate the proportion of asymptomatic infections in different countries and validate these estimates against empirical data.
• To assess the reliability of epidemic forecasts over time using relative error thresholds and effective prediction intervals.
• To analyze the role of the basic reproduction number $ R_0 $ in relation to observed trends in symptomatic and asymptomatic cases.

Proposed method

• Formulate the SQIARD model as an extension of the SIARD model, incorporating quarantine screening and transition rates from quarantined to infected or asymptomatic classes.
• Transform continuous differential equations into discrete-time difference equations to enable parameter training using historical infection data.
• Use FIR (Finite Impulse Response) algorithm to identify optimal model orders and train parameters based on validation sets of size 20.
• Calibrate model parameters using infection data from the US, South Korea, Brazil, India, Russia, and Italy, with special emphasis on US quarantine data for SQIARD.
• Evaluate forecast accuracy using relative error thresholds (5%, 10%, 20%) and define 'effective prediction intervals' as the number of days within each error margin.
• Compare SQIARD and SIARD forecasts over overlapping time windows to assess the impact of including quarantine dynamics on prediction precision.

Experimental results

Research questions

• RQ1 How does incorporating quarantine screening data into the SQIARD model improve forecast accuracy compared to the SIARD model?
• RQ2 What proportion of asymptomatic infections can be reliably estimated in different countries using the proposed models?
• RQ3 How do the trends in symptomatic and asymptomatic infections correlate with changes in the basic reproduction number $ R_0 $?
• RQ4 What is the effective prediction horizon of the models across diverse epidemiological contexts in six countries?
• RQ5 To what extent does the inclusion of quarantine dynamics enhance the model's ability to track real-time epidemic trends?

Key findings

• The SQIARD model achieved a 9-day effective prediction interval at 5% relative error for the US, outperforming the SIARD model’s 6-day interval.
• In Brazil, the SIARD model had only 1 day within 5% error, indicating poor short-term forecast reliability.
• For South Korea, the SIARD model predicted 2 days within 10% error, with $ R_0 $ values dropping below 1, suggesting epidemic control.
• Russia’s SIARD model achieved 15 days within 5% error, indicating strong model fit and reliable trend capture.
• Italy’s SIARD forecast showed decreasing $ I $ and $ A $ trends, with $ R_0 $ values below 1, supporting the conclusion of epidemic control.
• The model estimated 45% asymptomatic infections in Italy, closely matching the 43.2% reported in Vò, Italy, validating the model’s accuracy in estimating asymptomatic proportions.