key: cord-1024053-m9s1ecw5 authors: Kurita, J.; Sugawara, T.; Ohkusa, Y. title: First peak of COVID-19 outbreak in Japan might pass as of April 26, 2020 date: 2020-05-01 journal: nan DOI: 10.1101/2020.04.26.20081315 sha: b316e80fc5c41161252558fe188fcdcb01a476ab doc_id: 1024053 cord_uid: m9s1ecw5 Background: The COVID-19 outbreak has 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 difficulty, we constructed a mathematical model that can explain these phenomena. Method: We applied a susceptible-infected-model with the proportion of asymptomatic patients among the infected (q) as a key parameter for estimation as well as the basic reproduction number (R0). Results: We observed the first outbreak peak in Japan on April 3 for those infected on March 29 .Their R0 and q were estimated respectively as 2.048 and 99.987%. Discussion and Conclusion: By introducing a very high proportion of asymptomatic cases, two inconsistent phenomena might be resolved. This hypothesis should be verified through additional study. The initial case of COVID-19 in Japan was a patient who showed symptoms when returning from Wuhan, China on January 3, 2020. Subsequently, 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 people, but excluding those infected on a large cruise ship: the Diamond Princess [1] . In fact, the first peak was observed at the end of March. Subsequently, despite a declining epidemic curve, the Japanese government declared a state of emergency on April 7. The COVID-19 outbreak has two associated and inconsistent phenomena: its reproduction number is almost two; and it shows 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 Japan until the peak has been approximately 7000. A similar phenomenon was confirmed in Wuhan, China. How can one reconcile these two inconsistent characteristics of the outbreak of COVID-19? To resolve the difficulty, we constructed a mathematical model to explain the two phenomena. 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 was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.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 applied a simple susceptible-infected-recovery (SIR) model [2] [3] [4] to the epidemic curve of Japan and its 120 million population. We assume an incubation period that conforms to the empirical distribution in the early stage of the outbreak. The proportion of asymptomatic people among those infected (q) is a crucially important parameter for estimation in the model, as is the basic reproduction number (R 0 ). For simplicity, we assumed no infectiousness among asymptomatic cases. As data, we used the number of symptomatic patients reported by MLHW for January 14 -April 24 published [1] as of April 26. We excluded some patients who were presumed to be persons infected abroad or as passengers on the Diamond Princess. They were presumed not to be community-acquired 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. Onset dates were sometimes unreported. Therefore, we estimated the onset date. To do so, we inferred a distribution extending from onset to reporting based on patients for whom onset dates were available. Then we applied this empirical distribution to patients for whom onset dates were not available. Letting f(k) represent this empirical 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 1, 2020. . https://doi.org/10.1101/2020.04.26.20081315 doi: medRxiv preprint 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 delay leads to underestimation bias in the number of patients. Therefore, it must be adjusted as Similarly, patients for whom the onset dates were available are expected to be affected by the reporting delay. Therefore, we have M s |t where M s |t represents the reported number of patients for whom onset dates were within period s, extending until the current period t. We sought R 0 and q to fit the data to minimize the sum of the absolute values of discrepancies among the bootstrapped epidemic curve and the fitted values. The estimated distributions of the three reproduction numbers were calculated using 10,000 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 1, 2020. . https://doi.org/10.1101/2020.04.26.20081315 doi: medRxiv preprint fully replicated iterations of bootstrapping for the empirical epidemic curve of symptomatic patients. During January 14 -April 26 in Japan, 12,936 community-acquired cases were identified, excluding asymptomatic cases. Figure 1 depicts the empirical distribution of incubation period among 91 cases for which the exposure date and onset date were published by MHLW. The mode of the distribution 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. We observed the first peak of the outbreak as occurring with the April 3 onset date and March 29 infection date. Because Figure 3 depicts almost all cases reported up to 30 days, the first peak might not change over time. Therefore, we conclude that the first peak has already passed. It is noteworthy that no countermeasure was implemented when the peak was We applied a simple SIR model including the proportion of asymptomatic cases that had not been incorporated into the model to date. Earlier studies [5] [6] [7] have estimated R 0 for COVID-19 as 2.24-3.58 in Wuhan. Our obtained R 0 was similar but slightly smaller. Conversely, an earlier study [8] estimated R 0 in Japan as 0.6. That figure might lead to misguided policies for countermeasures in Japan. If results 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. Recently, Keio University Hospital reported that about 6% of newly administrated 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 1, 2020. . https://doi.org/10.1101/2020.04.26.20081315 doi: medRxiv preprint and non-COVID-19 patients were infected asymptomatically during April 13-19, 2020 [11]. During that period, Figure 1 implies that 2095 patients were reported, representing 11% (=2095 × 6985/120 millions) of the total population. The figure was slightly higher than 6%. However, they were not healthy people. Therefore, their protection against infection might be more of a concern; their usual activity might be less than that of healthy people. Therefore, incidence among those patients might be lower. The present study has some limitations. First, these results obtained with a very high proportion of asymptomatic cases are merely hypothetical. This hypothesis should be verified through additional study. Secondly, the peak 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 that second or third peak. One must particularly consider that April is the first month of the school year and the fiscal year in Japan. Consequently, the population in Japan reshuffles many of its activities at this time. Many new students and new employees move to Tokyo from outside Tokyo. Also, residents of Tokyo 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 will have to be postponed until 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 1, 2020. . https://doi.org/10.1101/2020.04.26.20081315 doi: medRxiv preprint outbreak ends. Thirdly, as described above, school closure and voluntary event cancellation are apparently effective. Therefore, their effects must be incorporated as effects influencing the model. Assessment of those effects constitutes our next challenge for future research efforts. Fourthly, for simplicity, we assumed no infectiousness of asymptomatic cases. However, another earlier study [9] found that such cases have equal infectiousness to that of symptomatic cases. We must modify the model for future studies. Fifthly, though we obtained very high proportion of asymptomatic cases, it may include some effect of under-ascertainment [12] . In other words, very mild cases probably were included as asymptomatic cases those who were not counted as infected in the present study. Isolation of those very mild cases and truly asymptomatic cases should be the next challenge. We found 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 , 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. 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. The results also explain aspects of the outbreak in Wuhan. Nevertheless, it is currently only a hypothesis. Its validity must be verified using data of outbreaks in other countries including China and the United States, or prefectures in Japan. The present study is based on the authors' opinions, but does not reflect any stance or policy of their professionally affiliated bodies. 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 1, 2020. . https://doi.org/10.1101/2020.04.26.20081315 doi: medRxiv preprint 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.