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 Omicron Variant
Omicron Variant
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Graduate School of Economics, Faculty of Economics, The University of Tokyo
Analysis
■Review of the previous projection (November 2)
■https://covid19outputjapan.github.io/JP/
■Hypothetical outlook if the Omicron variant does not exist
■Outlook if the Omicron variant is present
■Relationship between the basic reproduction number and the infection prevention effect of vaccine
■Relationship among the basic reproduction number, the rate of serious illness, and the number of seriously ill patients, given the infection prevention effect of vaccine
■Relationship among infection prevention effect of vaccine, the rate of serious illness, and the number of seriously ill patients, given the basic reproduction number
Important Points
■Infection trends in November and December were close to the optimistic scenario presented in the previous report (November 2)
■If the Omicron variant is not taken into account, the outlook for the number of infected and seriously ill patients is good, even taking into account the temporary spike in contact opportunities during the New Year holidays
■Spread of infections is likely to be slow over next 3 months
■It is unlikely that the bed utilization rate for seriously ill patients will exceed 50% in the next 3 months
■At this time, there is great uncertainty about the impact of the Omicron variant on the outlook for the number of infections and seriously ill patients
■Uncertainties regarding the basic reproduction numbers, the infection prevention effect of vaccine, and the rate of serious illness and mortality
Important Points
■The advent of the Omicron variant will worsen the outlook for infections, but the impact on the outlook for the number of seriously ill patients will depend on the rate of serious illness (for which data is still limited)
■Infection increases exponentially during the expansion phase, so the outlook for the number of seriously ill patients will worsen if the rate of serious illness does not drop significantly
■The equal curve of the number of seriously ill patients quantifies and visualizes this relationship
■If it gets worse, there is great uncertainty about the degree of worsening
■The possibility of a medical crunch sooner than the worst scenario presented in this report cannot be excluded
■Note that the following differences in factors need to be taken into account when considering the implications for Japan of information on the Omicron variant in other countries
■Rate of second vaccination. Vaccine manufacturer used (due to the different vaccine efficacy by manufacturers)
■Timing of the second vaccination (due to the presumption that the vaccine effectiveness decreases over time)
■Rate of third vaccination
■The way people come into contact with each other, and the degree of infection prevention measures taken at the individual level (e.g., the percentage of masks worn)
Important Points
■When considering policy, it is necessary to quantitatively evaluate both "risk of infection" and "risk to society, economy, culture, and education associated with behavioral restrictions"
■In this report, only the former risk is evaluated
■Optimal policy depends on judgments about how much value to relatively place on both of these aspects
■Therefore, the analysis in this report cannot give any suggestion about what policies should be implemented in the future
■From the perspective of "balancing infectious disease control and the social economy," it cannot always be said that "policies on the safe side from the perspective of infection control" are optimal
■Decreasing human contact and anxiety about the future may lead to sluggish consumption, resulting in unemployment, poverty, and increased inequality
■Decreasing human contact and anxiety about the future may lead to increased cases of suicides and decreased marriage and birth rates
■The media has "freedom of the press"
■An alarming article could be written based on the worst scenario in this report, or an article could be written to calm excessive anxiety by emphasizing that the degree of medical crunch depends on the rate of serious illness
Previous projection (November 2)
November 2 Projection (Tokyo)
Blue,·Black,·Red,·and Purple (Basic reproduction numbers 3, 3.75 [Basic Scenario], 5, 6)
November 2 Projection (Tokyo)
Hypothetical scenario if the Omicron variant does not exist
Setup
■Data until December 19 was used
■Analysis in Tokyo
■Recovery to "prepandemic levels of human contact and economic activity” over six months from January 2022
■Maximum number of newly infected patients per day that people can tolerate: 5,000
■Basic reproduction number of the Delta variant: 3, 3.75, 5, 6
■The value that the FujiiNakata team thinks which is most possible at this point is 3.75 (evidence: Analysis of "Steady State Contact Rate Parameters")
■Seasonality: Using the Sine function, the maximum value of the contact rate parameter in winter is set to 1.2 times the minimum value in summer
■Future rates of serious illness, deaths, and hospitalizations
■Weighted averages (using the number of infected patients) over the past 17 weeks
■See SPIMO (October) for more information on vaccine effectiveness
■Details are given on the last page of the Appendix
Settings (booster vaccination)
■Interval between second and third vaccinations: About 8 months
■Medical personnel: Assumed that 100% of the people who received their second vaccination on the week of March 10 (the date of the second vaccination) starts vaccinated in order, one week at a time from the first week of December
■Inoculation of the elderly, general public, and at workplaces: Assumed that 100% of the people who received their second vaccination on the week of May 3 (the date of the second vaccination) starts vaccinated in order, one week at a time from the first week of January
■First week of December 2021: Second vaccination recipients from the week of March 10, 2021 received third dose
■Second week of December 2021: Second vaccination recipients from the week of March 17, 2021 received third dose
■…
■First week of January 2022: Second vaccination recipients (medical personnel) from the week of April 14, 2021 receives third dose AND second vaccination recipients (elderly, general) of the week of May 3, 2021 receives third dose
■Second week of January 2022: Second vaccination recipients (medical personnel) from the week of April 21, 2021 receives third dose AND second vaccination recipients (elderly, general) of the week of May 10, 2021 receives third dose
Changes in Key Parameters
Changes in Key Parameters
* Weighted averages (based on the number of infected patients) over the past 17 weeks were used for the projection. November and December figures, when the number of infected patients remained at a very low level, were weighted to account for possible upward bias
Outlook without taking into account the Omicron variant: Basic reproduction numbers (3,·3.75 [Basic Scenario], 5, 6)
Analysis of the Omicron variant
Model
■Integrated SIR model considering the Delta and Omicron variants at the same time
■See Appendix for details
■Percentage of the Omicron variant is determined endogenously: (𝑁_𝑡^𝑜)/(𝑁_𝑡^𝛿+𝑁_𝑡^𝑜 )
Setup
■Assumed that 10 people are infected with the Omicron variant in Tokyo on December 26, 2021
■Relative basic reproduction numbers of the Omicron variant (relative to the Delta variant)
■1.0, 1.25, 1.5
■Relative Vaccine Efficacy of the Omicron variant (relative to the Delta variant)
■0.2, 0.6, 1
■Relative rate of serious illness of the Omicron variant (relative to the Delta variant)
■0.25, 0.5, 1
Equal curve of effective reproduction number (The relationship among basic reproduction number, infection prevention effect, and effective reproduction number)
■The red dot indicates that the effective reproduction number remained at about 1 from midNovember to midDecember with the Delta variant prevalent under some assumptions
■Some assumptions: Human flow is 80% compared with the steady state, basic reproduction number of the Delta variant is 3.125, 80% of the population has completed second vaccination, vaccine efficacy is 75%
■Note that the figure is not based on a simulation, but on a simple equation connecting to the above variables
■Each line represents a "pair of
■Equal curve of effective reproduction number visualizes the following (selfevident) fact
■When the basic reproduction number is consistent and VE decreases, the effective reproduction number increases
■Moving left from the red dot, it moves to a higher ERN line
■When VE is consistent and the basic reproduction number increases, the effective reproduction number increases
■Moving up from the red dot it moves to a higher ERN line
■If the basic reproduction number decreases and VE decreases, the effective reproduction number remains the same
■Consistent with the fact that each curve rises from left to right
The equal curve of the number of seriously ill patients (The relationship among the basic reproduction number, the rate of serious illness, and the number of seriously ill patients, given the infection prevention effect)
■Figure is based on a simulation
■VE against the Delta variant of second vaccination is 70%. BRN for the Delta variant is 3.75. For the rate of serious illness of the Delta variant, see "Changes in Key Parameters."
■The equal curve of the number of seriously ill patients (given a VE) quantifies and visualizes the following relationship
■If the basic reproduction number is low or the rate of serious illness is low (the lower to the bottom left in the figure), the number of seriously ill patients will be low at a certain time (the end of March in the figure)
■Each line indicates how much the rate of serious illness must decrease to maintain the number of seriously ill patients to a certain degree at the end of March when the basic reproduction number increases
■For example, in connection with the orange line, we can read the following
■Suppose the relative VE of the second vaccination against the Omicron variant is 0.6.
■If the basic reproduction number and the rate of serious illness of the Omicron variant are the same as those of Delta, the number of seriously ill patients at the end of March is 152
■Following the orange line, if the basic reproduction number of the Omicron variant is X times as that of the Delta variant, it can be read that how much the rate of serious illness must decrease to keep the number of seriously ill patients at 152 at the end of March
■Since the number of infected patients increases exponentially (during the expansion phase), even if the rate of serious illness decreases by a factor of X when the basic reproduction number increases by X, the number of seriously ill patients increases
■What can be said from the steep slope of the orange curve
The equal curve of the number of seriously ill patients (The relationship among infection prevention effectiveness, the rate of serious illness, and the number of seriously ill patients, given a basic reproduction number)
■Figure is based on a simulation
■VE against the Delta variant of second vaccination is 70%. BRN for the Delta variant is 3.75. For the rate of serious illness of the Delta variant, see "Changes in Key Parameters."
■The equal curve of the number of seriously ill patients (given a basic reproduction number) quantifies and visualizes the following relationship
■If VE is high or the rate of serious illness is low (the lower to the bottom right in the figure), the number of seriously ill patients will be low at a certain time (the end of March in the figure)
■Each line indicates how much the rate of serious illness must decrease to maintain the number of seriously ill patients to a certain degree at the end of March when VE is low
■For example, in connection with the orange line, we can read the following
■Suppose the relative basic reproduction number of the Omicron variant is 1.25 compared with the Delta variant
■If there is no change in VE and the rate of serious illness of the Omicron variant, the number of seriously ill patients at the end of March is 85
■Following the orange line, if the VE of the second vaccination against the Omicron variant is X times higher than the VE against the Delta variant (X < 1), it is indicated that how much the rate of serious illness must decrease to keep the number of seriously ill patients at 85 at the end of March
■Since the number of infected patients increases exponentially (during the expansion phase), even if the rate of serious illness decreases by X when the VE against the Omicron variant is X times higher (X < 1), the number of seriously ill patients increases
■What can be said from the steep slope of the orange curve
Various scenarios (relative BRN=1 for the Omicron variant)
■VE against the Delta variant of second vaccination is 70%. BRN for the Delta variant is 3.75. For the rate of serious illness of the Delta variant, see "Changes in Key Parameters."
Various scenarios (relative BRN=1.25 for the Omicron variant)
■VE against the Delta variant of second vaccination is 70%. BRN for the Delta variant is 3.75. For the rate of serious illness of the Delta variant, see "Changes in Key Parameters."
Various scenarios (relative BRN=1.5 for the Omicron variant)
■VE against the Delta variant of second vaccination is 70%. BRN for the Delta variant is 3.75. For the rate of serious illness of the Delta variant, see "Changes in Key Parameters."
Various scenarios (relative vaccine efficacy against the Omicron variant = 1.0)
■VE against the Delta variant of second vaccination is 70%. BRN for the Delta variant is 3.75. For the rate of serious illness of the Delta variant, see "Changes in Key Parameters."
Various scenarios (relative vaccine efficacy against the Omicron variant = 0.6)
■VE against the Delta variant of second vaccination is 70%. BRN for the Delta variant is 3.75. For the rate of serious illness of the Delta variant, see "Changes in Key Parameters."
Various scenarios (relative vaccine efficacy against the Omicron variant = 0.2)
■VE against the Delta variant of second vaccination is 70%. BRN for the Delta variant is 3.75. For the rate of serious illness of the Delta variant, see "Changes in Key Parameters."
■Analysis update and Zoom briefing on Tuesdays: https://Covid19OutputJapan.github.io/JP/
■Reference materials: https://covid19outputjapan.github.io/JP/resources.html
■Zoom briefing video: https://covid19outputjapan.github.io/JP/recording.html
■Economic Seminar Series
■https://note.com/keisemi/n/n9d8f9c9b72af
■https://note.com/keisemi/n/n7f38099d0fa2
■https://note.com/keisemi/n/nd1a6da98f00e
■Papers available at:https://link.springer.com/article/10.1007%2Fs42973021000984
■Twitter: https://twitter.com/NakataTaisuke
■Questions, requests for analysis, etc.
■taisuke.nakata@e.utokyo.ac.jp
Appendix: Model Details
Model (number of newly infected patients of the Omicron and Delta variants)
■For 𝑥∈{𝛿,𝑜}, For (the Delta and Omicron variants),
𝑁_𝑡^𝑥=𝐸𝑅𝑁_𝑡^𝑥 ∗(𝛾_𝑡^𝑥+𝛿_𝑡^𝑥 )∗𝐼_𝑡^𝑥,
𝐸𝑅𝑁_𝑡^𝑥=(𝑆_𝑡^𝑥)/(𝑃𝑜𝑝_0 ) 𝐵𝑅𝑁_𝑡^𝑥
𝐵𝑅𝑁_𝑡^𝑥=𝜌^𝑥 (𝛽_𝑡 (1−ℎ𝛼_𝑡 )^𝑘)/(𝛾_𝑡^𝑥+𝛿_𝑡^𝑥 )
𝛽_𝑡=3.5∗((𝛾_𝑡^𝛿+𝛿_𝑡^𝛿 ))/(1−ℎ𝛼_𝑡 )^𝑘 ∗seasonality_𝑡
𝜌^𝛿=1, 𝜌^𝑜∈{1.25, 1.5, 2.0}
■𝑁... newly infected patients, 𝑆 ... susceptible, 𝐼 ... infected patients, 𝑃𝑜𝑝_0 ... initial population
■𝛾... recovery rate , 𝛿 ... fatality rate, 𝛽 ... infection rate, 𝛼 ... economic loss rate
■𝜌... relative basic reproduction number
Model
■𝑥∈{𝛿,𝑜} For (the Delta and Omicron variants),
𝑆_(𝑡+1)^𝑥=𝑆_𝑡^𝑥−𝑁_𝑡^𝑥−𝜃^𝑥 𝑁_𝑡^(−𝑥)−𝐸𝑉_𝑡^𝑥
𝐸𝑉_𝑡^𝑥=𝜌_𝑣^𝑥 𝐸_1 𝑉_(1,𝑡−2)+𝜌_𝑣^𝑥 〖(𝐸〗_2−𝐸_1)𝑉_(2,𝑡−2)
𝐼_(𝑡+1)^𝑥=𝐼_𝑡^𝑥+𝑁_𝑡^𝑥−(𝜌_𝑑^𝑥 𝛿_𝑡^𝑥+𝛾_𝑡^𝑥 ) 𝐼_𝑡^𝑥
𝑅_(𝑡+1)^𝑥=𝑅_𝑡^𝑥+𝛾_𝑡^𝑥 𝐼_(𝑡+1)^𝑥+𝐸𝑉_𝑡^𝑥+𝜃^𝑥 𝑁_𝑡^(−𝑥)
𝐷_(𝑡+1)^𝑥=𝐷_𝑡^𝑥+𝜌_𝑑^𝑥 𝛿_𝑡^𝑥 𝐼_𝑡^𝑥
𝐼𝐶𝑈_(𝑡+1)^𝑥=𝐼𝐶𝑈_𝑡^𝑥−𝛾_𝑡^𝐼𝐶𝑈 𝐼𝐶𝑈_𝑡^𝑥+𝜌_𝑑^𝑥 𝛿_𝑡^(𝐼𝐶𝑈,𝑥) 𝐼_𝑡−𝜌_𝑑^𝑥 𝛿_𝑡^𝑥 𝐼_𝑡^𝑥
■𝑆 ... susceptible, 𝐼 ... Infected patients, 𝑅 ... immune, 𝐷 ... deceased, 𝐼𝐶𝑈 ... seriously ill patients,
■𝐸𝑉... people with immunity from vaccine, 𝑁 ... newly infected patients
■𝛾... recovery rate, 𝛿^𝐼𝐶𝑈 ... rate of serious illness, 𝛿 ... mortality rate
■𝜃... people with natural immunity from infection, 𝜌_𝑣 ... relative vaccine efficacy, 𝜌_𝑑 ... relative rate of serious illness
Model (declaration of a state of emergency)
■𝐼𝐶𝑈_𝑡^𝛿+𝐼𝐶𝑈_𝑡^𝑜>𝜅^𝑜𝑛 From the following week (when the number of seriously ill patients exceeds a certain number)
𝛽_𝑡=𝑐_1∗∑_(𝜏=𝑇−17+1)^𝑇▒𝛽_𝜏
𝛼_𝑡=𝛼^𝑜𝑛
■𝐼𝐶𝑈_𝑡^𝛿+𝐼𝐶𝑈_𝑡^𝑜<𝜅^off The state of emergency will be lifted and the situation will be resolved from the following week (if the number of seriously ill patients falls below a certain level)
𝛽_𝑡=𝜉_𝑡∗3.5∗(𝛾_𝑡^𝛿+𝛿_𝑡^𝛿 )∗𝑠𝑒𝑎𝑠𝑜𝑛𝑎𝑙𝑖𝑡𝑦_𝑡
𝜉_𝑡=max{1/(𝐷𝑅+1) (𝑡−𝑇_SoEoff )(1−𝑐_2 )+𝑐_2, 1}
𝛼_𝑡=min{𝛼_on+1/(𝐷𝑅+1) (𝑡−𝑇_SoEoff )(𝛼_off−𝛼_on ), 𝛼_off }
Initial value settings
■Initial values
■Determined 𝑅_0^𝑜,𝑆_0^𝑜 based on vaccine efficacy and retention rate of immunity against the Omicron variant among previously vaccinated and infected patients.
𝑅_0^𝑜=𝐸_1^𝑜 𝑉_1,0+(𝐸_2^𝑜−𝐸_1^𝑜 ) 𝑉_2,0+(𝐸_3^𝑜−𝐸_2^𝑜 ) 𝑉_3,0+𝜃(𝑅_0^𝛿−𝐸𝑉_0^𝛿 )
𝑆_0^𝑜=(𝑃𝑜𝑝_0−𝐷_0^𝛿 )−(〖𝐼_0^𝑜+𝑅〗_0^𝑜+𝐷_0^𝑜 )
𝐼_0^𝑜=10, 𝐷_0^𝑜=0
■The number of people who received a vaccination for the 𝑉_(𝑛,𝑡) ... 𝑛 time, and the efficacy of the 𝐸_𝑛^𝑜 ... 𝑛 th vaccination against the Omicron variant