Options for COVID-19 Countermeasures During the 7th Wave

・Analysis in Tokyo

・Setting that an increase in the use of hospital beds will change people’s behavior and force the suppression of infections
　・Information effect (fear effect), “voluntary changes in actions”

・We consider four policies
　・A1: No ordering of a quasi-state of emergency + current medical system
　・A2: No ordering of a quasi-state of emergency + expansion of medical system
　・B1: Ordering of a quasi-state of emergency + current medical system < following of handling during the 6th wave >
　・A2: Ordering of a quasi-state of emergency + expansion of medical system

・We analyze the policy effects in a hypothetical scenario in which the peak of infections during the 7th wave is twice that of the 6th wave under policy A1.
　・With B1 and B2, a quasi-state of emergency is ordered in the 5th week of July. It is lifted eight weeks later.

・Note that the scenarios presented are not worst-case scenarios (from the perspective of minimizing the number of infected people)

・Two important parameters of the analysis are the effects of a quasi-state of emergency and the effect of the rate of use of hospital beds on infections (information effect, fear effect).
　・We interpreted many empirical studies (including causal inference analysis) based on Japan data with regard to the effects of a quasi-state of emergency in light of the experiences of past waves, and made selections based on comprehensive judgment.
　　・Summary of the empirical analysis referred to: “Summary of empirical analysis of action restrictions and information effects” (Nakata and Okamoto, July 14, 2022)
　・We used the simple regression analysis described in “Details of analysis” for the information effect, fear effect and voluntary action changing effect.
　・Past analysis and experience suggest the following two points.
　　・Results suggest that the direct infection-control effect of action restriction policies may be limited, especially after a 2nd vaccination dose.
　　・The fear effect and voluntary action changing effect associated with an increase in the number of infected people and the rate of use of hospital beds may be relatively large.
　・We considered various parameters because of high uncertainty.

・Under Policy B1, we set the course of the basic reproduction number route to peak at twice the number of newly infected people as that of the 6th wave.
　・A quasi-state of emergency is ordered in the 5th week of July. It is lifted eight weeks later.
・We assumed that the number of hospital beds secured is 1.5 times the current number in scenarios involving expansion of the medical system.
　・The appendix also shows the results assuming that the number of hospital beds secured is 2.0 times the current number.
・Vaccination protection effect: 1st 5%, 2nd 30%, 3rd 50%, 4th 85%
・4th vaccination
　・Linear extrapolation based on the level of progress of the current vaccination rate
　・We assumed that 50% of the total population will be vaccinated in the end.
・Case fatality rate, rate of severe illness and rate of hospitalization during the 7th wave: see “Forecast of severe illness rate, case fatality rate and hospitalization rate during the 7th wave (revised version)” (Miyashita, Nakata, Okamoto, July 13, 2022, https://www.bicea.e.u-tokyo.ac.jp/wp-content/uploads/2022/07/NakataOkamoto_ICUDeath_20220713.pdf ）を参照

Expansion of medical system increases infection, because the use of hospital beds is less likely to increase, and the fear effect is diminished, making it difficult for behavioral inhibition to occur.

The case where the number of hospital beds doubled

　　　　Details of analysis

・We used a standard SIRD model.
・We obtained 𝑆_𝑡, 𝐼_𝑡, 𝑅_𝑡, and 𝐷_𝑡, from past new infections 𝑁_𝑡, number of new deaths 〖∆𝐷〗_𝑡, and the number of newly vaccinated people 〖∆𝑉〗_𝑡
・Using the obtained 𝑆_𝑡, 𝐼_𝑡 and 𝑁_𝑡, we calculated 𝛽_𝑡 (𝛽_𝑡=𝑁_𝑡/(𝑠_𝑡 𝐼_𝑡 ), 𝑠_𝑡=𝑆_𝑡/𝑃𝑜𝑝_0)
・With regard to policy A1, we determined exogenously 𝛽_𝑡 that achieves 𝑁_𝑡 (𝛽_𝑡^𝐴1)
・We simulated the rate of use of hospital beds based on that 𝛽_𝑡.
・Based on the slope obtained by regression (to be described later) and the rate of bed use for severely ill patients with lag (Tokyo, new standard), we calculated the predicted value 𝛽_𝑡 of 𝛽 ̂_𝑡, and calculated the divergence with the 𝛽_𝑡 determined exogenously.
　　　　　　　　　　　　　　　　　𝛽 ̂_𝑡^𝐴1=𝛼_0+𝛼_2 (〖𝐼𝐶𝑈〗_𝑡^𝐴1)/〖𝐼𝐶𝑈〗_𝑚𝑎𝑥
　　　　　　　　　　　　　　　　　𝜀_𝑡^𝐴1=𝛽_𝑡^𝐴1−𝛽 ̂_𝑡^𝐴1
・We assumed that 𝛼_2 is independent of a quasi-state of emergency so the 𝛽 ̂_𝑡 equation does not include the trend that is the effect of a quasi-state of emergency.

・Specification 1: We regressed 𝛽_𝑡 during the last quasi-state of emergency period in Tokyo (January 21 to March 21, 2022) to 〖𝐼𝐶𝑈〗_𝑡/〖𝐼𝐶𝑈〗_𝑚𝑎𝑥 with intercept and lag, and trend  〖(𝐼𝐶𝑈〗_𝑡 : a lag exists in terms of the number of severely ill patients at the start of week 𝑡).
　　　　　　　　　　　　　　　　　𝛽_𝑡=𝛼_0+𝛼_1 𝑡+𝛼_2 〖𝐼𝐶𝑈〗_𝑡/〖𝐼𝐶𝑈〗_𝑚𝑎𝑥 +𝜀_𝑡
・The rate of vaccination rates was not included in the regression equation because it was already taken into account when we calculated 𝑆_𝑡.
・Variants are largely described as a function of time and are not included in the regression equation because of multicollinearity with trends.
・𝛼_0: 2.0500 (0.2306), 𝛼_1: -0.0296 (0.0781), 𝛼_2: -3.8372 (1.8114)

・Specification 2: We used data from December 2020 and a dummy declaration of a state of emergency / quasi-state of emergency (𝐷𝑢𝑚𝑚𝑦_𝑡) to measure the effect of the ICU bed use rate with lag 〖𝐼𝐶𝑈〗_𝑡/〖𝐼𝐶𝑈〗_𝑚𝑎𝑥  .
　　　　　　　　　　　　　　　　　𝛽_𝑡=𝛼_0+𝛼_1 𝐷𝑢𝑚𝑚𝑦_𝑡+𝛼_2 〖𝐼𝐶𝑈〗_𝑡/〖𝐼𝐶𝑈〗_𝑚𝑎𝑥 +𝜀_𝑡
・𝛼_0: 1.6853 (0.2917), 𝛼_1: -0.4396 (0.4234), 𝛼_2: -1.2536 (0.8688)

・With the baseline, we used the average of the estimated values of Specification 1 and Specification 2.
　・Specification 1 and Specification 2 correspond to fear effect large and fear effect small, respectively.

・We assumed that 𝛽_𝑡 would reduce by 𝑥% over the period due to a quasi-state of emergency.
・We assumed that the number of usable hospital beds would increase by a factor of c due to expansion of the medical system.
・We used the already obtained divergence 𝜀_𝑡^𝐴1, to obtain 𝛽_𝑡 under a certain policy as follows:
　　　　　　　　　　　　　𝛽_𝑡^𝑃𝑜𝑙𝑖𝑐𝑦=(𝛼_0+𝛼_2 (1/𝑐) 〖𝐼𝐶𝑈〗_𝑡/〖𝐼𝐶𝑈〗_max +𝜀_𝑡^𝐴1 )(1−𝕀_(mambo,𝑡 ) 𝑥)

・Taisuke Nakata is supported by JSPS Grant-in-Aid for Scientific Research (KAKENHI), Project Number 22H04927, the Research Institute of Science and Technology for Society at the Japan Science and Technology Agency, COVID-19 AI and Simulation Project (Cabinet Secretariat), the Center for Advanced Research in Finance at the University of Tokyo, and the Tokyo Center for Economic Research.

・Research papers and policy reports
　・https://www.bicea.e.u-tokyo.ac.jp/
　・https://covid19-icu-tool.herokuapp.com/
　・https://covid19outputjapan.github.io/JP/resources.html