Correlations between Corona Infection and Human Flow

■Infections spread rapidly in late July and early August in Tokyo
■Claims heard at the time
　■"Without a lockdown, infection suppression will be difficult"
　■"We need to reduce human flow by 50% to reduce infection"
■Infections have declined rapidly despite an increase in various human flow data since late August
■Simple questions
　■Is there a connection between human flow and infection?
　■Are lockdowns and state of emergency necessary to control infection?
　■Have the previous state of emergency been effective?

■Analyzing the correlation between data related to human flow and infections in Tokyo
　■Various data related to human flow
　■Presence/absence/strength of correlation
　■Stability of correlation

■Data that correlates with infection other than human flow
　■Atmospheric temperature
　■Period (Monthly Dummy, Sine Curve)
　■Whether or not a state of emergency has been declared
　■Hospital bed utilization rate for seriously ill patients

■Some variables have low correlation, some have high correlation
　■Examples of high correlation variables: Google Mobility (retail and entertainment), people staying in major downtown areas at night, Ginza (Location Mind)
　■Examples of low correlation variables: Google Mobility (grocery stores and pharmacies), Self-restraint Rate Index (20s), Tokyo Station (Location Mind)
■Even in highly correlated cases, the "unexplainable part" is large
　■The explanatory power (R2) of the variation in the effective reproduction number of the highly correlated variables is about 0.6. That means 40% cannot explained
　■The root mean square error of prediction (RMSE) for the number of new infections two weeks ahead is more than 500. At the most, the margin of error is more than 1,000 people
■Even in highly correlated cases, the correlation is not necessarily stable
■There are other variables that are highly correlated besides human flow

■Theoretically, the infections spread through person-to-person contact
■Empirically, some data related to human flow are somewhat strongly correlated with infection
　■However, the correlation is not always stable. Moreover, "correlation does not = causation"
■Guidelines for policy analysis
　■Monitoring data related to human flow is important
　■However, it is not desirable to rely solely on human flow data. Other determinants of infection should also be considered
　　■"(August 10) Scenario for controlling the spread of infection through voluntary behavior change" https://covid19outputjapan.github.io/JP/tokyo_20210810.html
　　■"(Forthcoming) Factors behind the infection decrease in Tokyo: quantitative analysis"
　■There are many factors that can affect infection
　　■Analysts tend to rely on "what can be measured." However, "what can be measured" is not always the most important
　　■In policy analysis, it is important to analyze and interpret the results of analysis while taking into account the importance of "things that cannot be measured"
　　■In policy analysis, it is desirable to analyze from various perspectives, not just one

■Infection may decline rapidly without lockdown/additional restriction on human flow
■Lessons
　■Going forward, we should be more cautious than ever about lockdowns and restriction on human flow
　　■Why? (1) Because the uncertainty of the effects of policies to restrict human flow has increased.
　　　(2) Because these policies have significant costs (negative impact on society, economy, culture, and education)
　■This does not necessarily mean that they should be excluded from policy options altogether
　　■"Infection can be reduced without additional restriction on human flow" is not the same as "restriction on human flow is not always helpful in reducing infection"
　　■If it is thought that reducing human flow is effective in reducing infection, and if measures can be taken to mitigate the negative effects of this, they can be considered
　　　■In that case, evidence regarding the causal relationship should be presented as much as possible

■Time-series data on the effective reproduction number in Tokyo obtained from Toyo Keizai Online*
　■See Appendices for details of effective reproduction numbers in Toyo Keizai
■The baseline effective reproduction number rises with the spread of mutated variants, while it declines with the distribution of vaccination
　■Discounting the impact of these two factors to allow comparison of the effective reproduction number at different times
　■This "Adjusted Effective Reproduction Number" was used
　■Details of the adjustment method are given in the Appendices
■Assumption regarding mutated variants
　■Infectivity of Alpha variant: 1.3 times that of the conventional variant
　■Infectivity of Delta variant: 1.5 times that of Alpha variant
■Assumptions about the vaccines
　■50% gain immunity 1 week after 1st vaccination
　■80% gain immunity 1 week after 2nd vaccination
*Toyo Keizai Online "Coronavirus Disease (COVID-19) Situation Report in Japan "https://toyokeizai.net/sp/visual/tko/covid19/

■A lagged linear regression model was created with the log series of the adjusted effective reproduction number as the objective variable.
　■The time lag is mainly due to the incubation period of the virus plus the lag between onset and reporting
　■Thereafter, the correlation coefficient and the coefficient of determination are calculated for the logarithmic series of the effective reproduction number and the human flow data from 2 weeks earlier

log⁡(𝐸𝑅𝑁_𝑎𝑑𝑗 (𝑡))=𝑎_0+𝑎_1 𝑀𝑜𝑏𝑖𝑙𝑖𝑡𝑦(𝑡−𝑙𝑎𝑔_𝑒 )+𝑎_2 𝑋(𝑡−𝑙𝑎𝑔_𝑒)+𝜖
𝐸𝑅𝑁_𝑎𝑑𝑗 : Adjusted Effective Reproduction Number (see Appendices for adjustment method)
𝑀𝑜𝑏𝑖𝑙𝑖𝑡𝑦 : Human Flow Data, 𝑋 : Explanatory variables other than human flow (seasonality, cyclicality, bed utilization rate for seriously ill patients, state of emergency)
𝑎_0 : Constant items, 𝜖 : Error items
𝑙𝑎𝑔_𝑒 : Time lag before human actions are observed in the effective reproduction numbers (set to 2 weeks)

■In creating the regression equation, the following studies were referred to.
Nouvellet, P., Bhatia, S., Cori, A. et al. Reduction in mobility and COVID-19 transmission. 
Nat Commun 12, 1090 (2021).
https://doi.org/10.1038/s41467-021-21358-2

Example of data with high correlation

Example of data with low correlation

※Converted to the number of new cases based on the definition of effective reproduction number (see Appendices).

Rolling Window for 3 months

Rolling Window for 6 months

Examples of data that have high correlation coefficients but seem to have no causal relationship

※Period covered: 6 months from 2020/09/01 to 2021/02/28 (excluding days that no measurement was made)
Using Google Community Mobility Report (https://www.google.com/covid19/mobility/)

※Synthesized sine waves with cycles of 100, 200, and 400 days

■Analysis updated weekly on Tuesdays
　https://Covid19OutputJapan.github.io/JP/

■Questions, requests for analysis, etc.
　■dfujii@e.u-tokyo.ac.jp
　■taisuke.nakata@e.u-tokyo.ac.jp

■Relationships between variables involved in macroeconomics are often unstable
　■Inflation rate and Unemployment rate (Phillips curve)
　■Relationship between Interest rates and Consumption/Investment
　■Relationship between JGB Holding Amount and JGB Interest rate

■There is a vast amount of empirical and theoretical research on how these relationships have changed

Rolling Window for 3 months

Rolling Window for 6 months

Seasons

Cycles

State of emergency

Degree of Pressure on Medical System

※Synthesized sine waves with cycles of 100, 200, and 400 days

■Humidity：https://www.data.jma.go.jp/gmd/risk/obsdl/
■Google Mobility：https://www.google.com/covid19/mobility/
■Location Mind：https://locationmind.com/
■Mutated Variant rates：https://www.mhlw.go.jp/content/10900000/000816622.pdf p.112
■Self-restraint Rate Index：https://www.yomiuri.co.jp/topics/covid19/japan-confirmed-cases-on-map/
■Number of seriously ill patients, number of beds for seriously ill patients, and number of vaccinations：https://stopcovid19.metro.tokyo.lg.jp/
■Effective Reproduction Number：https://toyokeizai.net/sp/visual/tko/covid19/
■Number of people staying in major downtown areas：https://www.igakuken.or.jp/r-info/monitoring.html#monitoring

■Developed by Professor Hiroshi Nishiura of Kyoto University and his team.
■https://toyokeizai.net/sp/visual/tko/covid19/
■It is characterized by its simplicity and ease of calculation by anyone, as it emphasizes real-time performance. It is also used in materials reported to the Ministry of Health, Labour and Welfare and Advisory Board.
■See the following slides for derivation methods
■https://github.com/contactmodel/COVID19-Japan-Reff/blob/master/nishiura_Rt%E4%BC%9A%E8%AD%B0_12May2020.pdf

𝐸𝑅𝑁(𝑡):=(𝑁(𝑡)/𝑁(𝑡−1) )^((𝑀𝑒𝑎𝑛 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒)/(𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑟𝑒𝑝𝑜𝑟𝑡𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 " " ))

N(t) : Number of new infections in week t, Length of reporting time : Reporting Interval,
Mean generation time : Mean generation time (the time it takes from infection of the source to infection of the secondary infected person)

Assuming that Mean generation time = 5 days, length of reporting time = 7 days.

Basic Concept
1) If mutated variants had not spread... (2) If vaccine had not been distributed...
⇨ Calculate what the effective reproduction number would have been

𝐸𝑅𝑁_𝑎𝑑𝑗 (𝑡)=(𝐸𝑅𝑁_𝑇 (𝑡))/((1−𝑉𝑆(𝑡−𝑙𝑎𝑔_𝑒))∗𝑉𝐸(𝑡−𝑙𝑎𝑔_𝑒))

𝑉𝑆(𝑡)=𝑣𝑒_1 (𝑉_1 (𝑡−𝑙𝑎𝑔_𝑣 )−𝑉_2 (𝑡−𝑙𝑎𝑔_𝑣))/𝑃𝑂𝑃+𝑣𝑒_2 (𝑉_2 (𝑡−𝑙𝑎𝑔_𝑣 ))/𝑃𝑂𝑃

𝑉𝐸(𝑡)=(1−𝑟_𝛼 (𝑡)−𝑟_𝛿 (𝑡))+𝑅_𝛼 𝑟_𝛼 (𝑡)+𝑅_𝛿 𝑟_𝛿 (𝑡)

𝐸𝑅𝑁_𝑎𝑑𝑗 : Adjusted Effective Reproduction Number, 𝐸𝑅𝑁_𝑇 (𝑡) : Effective Reproduction Number (Toyo Keizai),
𝑉𝑆 : Rate of Immunity Acquisition, VE : Mutated Variants Effects
𝑉_1 : Number of Vaccinations (1st dose), 𝑉_2 : Number of Vaccinations (2nd dose), 𝑃𝑂𝑃 : Population of Tokyo
𝑟_𝛼 : Alpha Variant Percentage, 𝑟_𝛿 : Delta Variant Percentage

Parameter List