key: cord-0934573-isbw3h1v authors: Kurita, J.; Sugawara, T.; Ohkusa, Y. title: Asymptomatic infection and herd immunity of COVID-19 in Wuhan and Japan date: 2020-05-06 journal: nan DOI: 10.1101/2020.05.01.20087155 sha: f01cfce7edea39a551465b328021c77374a33fcd doc_id: 934573 cord_uid: isbw3h1v Background: The COVID-19 outbreak has shown two inconsistent phenomena: its reproduction number is almost two; and it shows earlier and lower peaks for new cases and the total number of patients. Object: To resolve this inconsistency, we constructed a mathematical model to explain these phenomena. Method: To outbreak data from Wuhan, China and Japan, we applied a susceptible-infected-recovery model with the proportion of asymptomatic patients among infected people (q) as a key parameter for estimation, along with the basic reproduction number (R0). Results: The first outbreak peak was recorded in Japan on April 3 for those infected on March 29. Their R0 and q were estimated respectively as 3.19 and 99.32% in Wuhan. In Japan, these were estimated around the peak as 2.96 and 99.99%. Discussion and Conclusion: By introducing a very high proportion of asymptomatic cases, the two inconsistent phenomena might be resolved. Especially in Japan, the asymptomatic cases were 60 times higher than those of China. The COVID-19 outbreak emerged in Wuhan, China on December 1 [1] . Approximately 50,000 cases in all were reported by March 6 [2] . The initial case of COVID-19 in Japan was a patient who showed symptoms when returning from Wuhan, China on January 3, 2020. As of April 26, 2020, the Ministry of Labour, Health and Welfare (MLHW) in Japan announced that there were 7,741 cases in Japan, including asymptomatic but infected people, but excluding those infected on a large cruise ship: the Diamond Princess [3] . In fact, the peak in Wuhan occurred on February 12. In Japan, the first peak was observed at the end of March. Subsequently, despite a declining epidemic curve, the government declared a state of emergency in Japan on April 7. The COVID-19 outbreaks have two associated and inconsistent phenomena: their respective reproduction numbers are almost two; and outbreaks show earlier and lower peaks of new cases and the total number of patients. That reproduction number of two indicates that the peak will be reached when half of the population is infected. However, the total number of patients in Wuhan up to the peak was around 48,000. In Japan, the peak was reached after approximately 7000 cases. A similar phenomenon was confirmed in South Korea. How can one reconcile these two inconsistent characteristics All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 6, 2020. . https://doi.org/10.1101/2020.05.01.20087155 doi: medRxiv preprint community-acquired infection in Japan. For onset dates of some symptomatic patients that were unknown, we estimated their onset date from an empirical distribution with duration extending from the onset to the report date among patients for whom the onset date had been reported. The Wuhan data included no reported onset date for any patient. Therefore, we applied the empirical distribution of duration between onset to report in Japan to them. We estimated the onset date of patients whose onset dates were not reported as follows: Letting f(k) represent this empirical distribution and letting N t denote the number of patients for whom onset dates were not available published at date t, then the number of patients for whom the onset date was known is t-1. The number of patients for whom onset dates were not available was estimated as f(1)N t . Similarly, the number of patients with onset date t-2 and whose onset dates were not available were estimated as f(2)N t . Therefore, the total number of patients for whom the onset date was not available, given an onset date of s, was estimated as Σ k=1 f(k)N s +k for the long duration passing from s. Moreover, the reporting delay for published data from MHLW might be considerable. In other words, if s+k was larger than that in the current period t, then s+k represents the future for period t. Therefore, Ns+k was not observable. Such a reporting All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 6, 2020. . https://doi.org/10.1101/2020.05.01.20087155 doi: medRxiv preprint reached a peak and began a monotonic decreasing trend. Therefore, we inferred different reproduction numbers for the three periods. We assign R 0 to the period before VECSC , R v to the VECSC period, and R a to the period after VECSC. During January 20 through March 5 in Wuhan, 68,289 patients were reported. During January 14 -April 26 in Japan, 12,936 community-acquired cases were identified, excluding asymptomatic cases. Figure 4 depicts the empirical distribution of incubation periods among 91 cases whose exposed date and onset date were published by MHLW in Japan. Its mode was six days. The average was 6.6 days. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Figures 2 and 3 also include the fitted line based on estimated parameters in Wuhan and Japan. We observed the peak in Wuhan as February 7. The epidemic curve was apparently unaffected by blocking of traffic, which started on January 23. Moreover, the peak was two weeks later than the introduction of lockdown. Therefore, most patients whose onset contributed to the peak were infected after blocking of traffic. The peak is probably not the result of the blocking of traffic. We observed the first peak of the outbreak in Japan as occurring with the April 3 onset date and the inferred March 29 infection date. Because Figure 1 depicts almost all cases reported up to 30 days, the first peak might not change over time. Therefore, we conclude that the first peak of outbreak in Japan has already passed. It is noteworthy that no countermeasure was implemented when the peak was reached, which occurred after VECSC period. Moreover, a state of emergency was declared on April 7. During March 21 through April 6, the only measure was a All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 6, 2020. . https://doi.org/10.1101/2020.05.01.20087155 doi: medRxiv preprint recommendation that events with large audiences or numerous participants be cancelled. Therefore, the peak infection date of the end of March can not be regarded as a result of strong countermeasures in Japan. Nevertheless, VECSC has apparently been effective because the epidemic curve is below the fitted line, as shown by the model in Figure 4 . Moreover, the end of March might be an almost identical climate to that of the beginning of March. Results therefore suggest that temperature and humidity might not affect the virus infectiousness. We applied a simple SIR model including the proportion of asymptomatic cases that had not been incorporated into the model to date. Therefore, this is the first model which can show a peak and declining phase without a change in the reproduction number for COVID-19 outbreak. Figures 2 and 3 prove that the model fits well in Wuhan and Japan. Earlier studies [8-10] have estimated R 0 for COVID-19 as 2.24-3.58 in Wuhan. Our obtained R 0 was similar but slightly smaller. By contrast, an earlier study [11] estimated R 0 in Japan as 0.6. That figure might foster misguided policies for countermeasures in Japan. If results of the present study are correct, then they would necessitate adherence to contact tracing to detect clusters when more than 60 million people would become infected. All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. We estimated the proportion of asymptomatic cases among infected people as 99.32 and 99.98%, respectively, in Wuhan and Japan, which means that the respective ratios of asymptomatic cases to symptomatic cases were 147.8:1 and 8941:1. In other words, for every symptomatic patient confirmed, approximately 150 or 9000 asymptomatic cases are presumed to exist. A report of an earlier study [7] described the proportion of asymptomatic cases among infected people as 3/23. That proportion represents a huge difference from our results presented herein. A possible reason might be laboratory test procedures. Earlier studies used PCR tests, which detected infection at the time of specimen collection. Therefore, a negative PCR test result does not contra-indicate a past infection. To confirm our results through laboratory testing, complete laboratory-based surveillance in the community using an IgG antibody test, not PCR, is expected to be necessary. Such a trial was launched in New York City. It revealed from antibody testing that about 15% of residents were positive [12] . At that time, the prevalence was reported as 0.88% in New York state. Therefore, q was 94% in New York state. That result might be similar to our results obtained for q. Recently, Keio University Hospital reported that about 6% of newly administrated and non-COVID-19 patients were infected asymptomatically during April 13-19, 2020 All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 6, 2020. . https://doi.org/10.1101/2020.05.01.20087155 doi: medRxiv preprint hypothesis should be verified through additional study. Secondly, the peak in Japan on April 2 might be only the first peak: a second and third wave might occur. Moreover, a second or third wave peak might be higher than the first peak. In fact, the peak of the entire outbreak might eventually be such a second or third peak. One must particularly consider that April is the first month of the school year and the fiscal year in Japan. For that reason, the population in Japan reshuffles many of its activities at this time. Many new students and new employees move to Tokyo from outside Tokyo. In addition, Tokyo residents move away from the city. Therefore, the outbreak can be expected to increase again in middle or late April. Evaluation of the outbreak of COVID-19 in Japan in its entirety must be postponed until the outbreak ends. Thirdly, as described above, VECSC is apparently effective. Therefore, its effects must be incorporated as effects influencing the model. Assessment of those effects constitutes our next challenge for future research efforts. Fourthly, although we obtained a very high proportion of asymptomatic cases, they might include some effects of under-ascertainment [15] . Under-ascertainment was estimated as 9% in Wuhan. In other words, about 10 times in the estimated about 150 times of the reported cases were probably mild cases. In that sense, 140 times of the All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 6, 2020. . https://doi.org/10.1101/2020.05.01.20087155 doi: medRxiv preprint reported cases were asymptomatic cases in Wuhan. What about Japan? Under-ascertainment might be related to the strategy of PCR testing. Investigation of that possibility is anticipated as a future challenge for study. Fifthly, although the distribution of incubation periods is probably almost identical in Wuhan and Japan, the distribution of the delay from onset to report might be much different. It might be affected by testing procedures and capacity, reporting systems, and human resources to apply them. We do not know the distribution in Wuhan. However, we must evaluate the inference that the distributions were the same. Results indicate that that the first peak of COVID-19 outbreak was April 2. The central government of Japan declared an emergency on April 7. However, as shown in Figure 1 , the number of symptomatic patients had already declined. Probably, the declaration served to mitigate the outbreak. By introducing a very high proportion of asymptomatic cases, two inconsistent phenomena might be resolved as a result of this study: the high reproduction number and low peak. Nevertheless, it is currently only a hypothesis. Its validity must be All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 6, 2020. . https://doi.org/10.1101/2020.05.01.20087155 doi: medRxiv preprint verified using data of outbreaks of prefectures in Japan, or from other countries including the United States. The present study is based on the authors' opinions, but does not reflect any stance or policy of their professionally affiliated bodies. 2 2 2 4 2 6 2 8 3 0 1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 2 4 J a n F e b M a r All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 6, 2020. 1 8 2 2 2 6 3 0 3 7 1 1 1 5 1 9 2 3 2 7 2 6 1 0 1 4 1 8 2 2 2 6 3 0 3 7 1 1 1 5 1 9 2 3 2 7 J a n F e b M a r A p r All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 6, 2020. . https://doi.org/10.1101/2020.05.01.20087155 doi: medRxiv preprint All rights reserved. No reuse allowed without permission. was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint (which this version posted May 6, 2020. . https://doi.org/10.1101/2020.05.01.20087155 doi: medRxiv preprint Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China. Lancet Situation of novel corona virus pneumonia in Hubei province Japan Ministry of Health, Labour and Welfare Preliminary evaluation of voluntary event cancellation as a countermeasure against the COVID-19 outbreak in Japan as of 11 Forecast of the COVID-19 outbreak, collapse of medical facilities, and lockdown effects in Tokyo Real-time estimation and prediction for pandemic A/H1N1(2009) in Japan We acknowledge the great efforts of all staff at public health centers, medical institutions, and other facilities who are fighting the spread and destruction associated with COVID-19.