[Paper Review] Space-time dependence of corona virus (COVID-19) outbreak

Kathakali Biswas, Parongama Sen|arXiv (Cornell University)|Mar 6, 2020

COVID-19 epidemiological studiesMathematics18 references58 citations

TL;DR

The paper analyzes global COVID-19 outbreak data using a SIR model on Euclidean networks and examines spatial correlations, finding an approximate inverse-square relation between case counts and distance from Wuhan and separate growth patterns for China and the rest of the world.

ABSTRACT

We analyse the data for the global corona virus (COVID-19) outbreak using the results of a previously studied Susceptible-Infected-Removed (SIR) model of epidemic spreading on Euclidean networks. We also directly study the correlation of the distance from the epicenter and the number of cases. An inverse square law is seen to exist approximately. The studies are made for China and the rest of the world separately.

Motivation & Objective

• Motivate studying COVID-19 spread with a Susceptible-Infected-Removed (SIR) framework on a spatial network.
• Analyze cumulative and daily case data separately for China and the rest of the world (ROW).
• Fit empirical growth forms to China and ROW data and compare with network-based spreading models.
• Investigate spatial dependence by correlating case counts with distance from Wuhan.
• Explore temporal patterns and two transmission modes (local vs imported) in ROW.

Proposed method

• Apply a previously studied SIR model on Euclidean networks with distance-decaying transmission to fit cumulative COVID-19 data.
• Fit China cumulative cases to R_Ch = A_Ch exp(t/T_Ch) / [1 + B_Ch exp(t/T_Ch)], obtaining A_Ch ≈ 2000, T_Ch = 5.3 ± 0.27, B_Ch = 0.02.
• Fit ROW cumulative cases to R_ROW = A_ROW exp(t/T_ROW) + R_0, obtaining A_ROW ≈ 2, T_ROW = 4.93 ± 0.06, R_0 ≈ 122.
• Compute Haversine distances from Wuhan to other locations and analyze case counts versus distance, noting an approximate d^{-2} dependence for China.
• Examine the date of first infection in ROW versus distance from Wuhan to distinguish local vs imported transmission clusters.
• Discuss data limitations and data-driven interpretation of multiple peaks in newly infected cases.

Experimental results

Research questions

• RQ1 Does the cumulative COVID-19 data for China and ROW follow distinct growth forms consistent with SIR-like dynamics?
• RQ2 Is there a measurable spatial dependence of case counts on distance from the Wuhan epicenter, and if so, what is its form?
• RQ3 Can the spread patterns be reconciled with an SIR model on a Euclidean network with distance-dependent transmission?
• RQ4 What are the temporal patterns of first infections in ROW in relation to distance, indicating local versus imported transmission?

Key findings

• China’s cumulative cases fit the empirical form R_Ch = A_Ch exp(t/T_Ch) / [1 + B_Ch exp(t/T_Ch)] with A_Ch ≈ 2000, T_Ch = 5.3 ± 0.27, B_Ch = 0.02.
• ROW’s cumulative cases fit R_ROW = A_ROW exp(t/T_ROW) + R_0 with A_ROW ≈ 2, T_ROW = 4.93 ± 0.06, R_0 ≈ 122.
• The cumulative number of cases versus distance from Wuhan shows an approximate inverse-square law d^{-2} in China, with some scatter when including ROW.
• Correlation between distance and affected cases is modest (China: -0.267, ROW: -0.197).
• Data suggest two clusters in ROW: local transmission and imported infections, with dates reflecting different transmission modes.
• The timescales for China and ROW are similar, consistent with the same virus affecting both regions.