key: cord-0299464-dh0nwir7 authors: Tomie, T. title: PCR test positive rate revealing the real infection epidemic status examined in the COVID-19 epidemic in Tokyo, Japan date: 2021-09-21 journal: nan DOI: 10.1101/2021.09.15.21263609 sha: 48b4f3937a8d4cd9c7e3d9b78247b2ac6f7c67e3 doc_id: 299464 cord_uid: dh0nwir7 In order to come up with effective infectious disease countermeasures, we need a method to evaluate the effectiveness of the countermeasures. As the most reliable epidemic diagnosis, we propose the PCR test positive rate. Examining the COVID-19 epidemic in Tokyo shows that the positive rate follows the epidemic accurately, without being affected by medical institution closures or the psychology of people. By comparing with the change of the positive rate, we argue that the psychology of people was the cause of the observed asymmetry and shallow valleys in the number of confirmed cases. We discuss that the positive rate as large as 1-5% in the valleys of the epidemic implies that many people are already infected and immune. The observed fact that the positive rate followed the number of positives accurately and the value lower than those reported in the test-negative design studies of influenza are attributable to the government policy of finding as many patients as possible. We mention three possibilities as the causes of the repeated COVID-19 epidemic in Japan. People's actions were restricted by such as lockdowns of cities to control COVID-19 infection. To evaluate the effectiveness of countermeasures, we need to understand the status of the infection epidemic correctly and promptly. It is common to analyze the number of the PCR (polymerase chain reaction) test positives. The first COVID-19 epidemic in Wuhan ended as forecasted by analyzing the change in the number of positives (ref.1). However, there are some problems in the use of PCR test positives. The major problem is that we cannot wipe out the doubts about whether the number of PCR test positives correctly reflects the epidemic. It is not easy to find all potentially infected people including asymptomatic people, but it is not necessary. To estimate the effectiveness of the disease control, it is sufficient for any index to be in proportion to the epidemic. However, it is not easy to verify whether the index reflects the real epidemic. When forecasting the end of the ever-first COVID-19 epidemic in Wuhan, we found that the number of infected people announced was initially lower than the forecast curve (ref.2). Our speculation is the following. Initially, people did not pay much attention to the disease, resulting in fewer PCR tests and not finding certain infected people. On the other hand, when p. 2 people hear the news that the number of confirmed cases is increasing sharply, people might become anxious about their infection, and many people may take PCR tests. An increase in the PCR tests increases the number of positives, making the number of positives un-proportional to the epidemic. Thus, the number of PCR test positives might be affected by the psychology of people. The number of positives also fluctuates due to the non-constant testing capacity of medical and testing institutions and the processing capacity of test result processing institutions. On holidays and public holidays, the number of inspections reduces significantly. More people will visit hospitals before and after holidays, and the number of positives can be larger before and after holidays. For reducing this fluctuation, it is common to perform a 7-day moving average, but a long-term moving average impairs the time resolution of the information of the epidemic and hinders the correct evaluation of the effect of policy. The author devised a day of the week correction method as a smoothing method that does not impair the time resolution. If the number of tests reduces every Sunday, for example, to a half, the fluctuation can be smoothed out by doubling the number. This method provides a smooth epidemic curve without the time resolution being impaired. However, it is not easy to compensate for the effects of holidays other than Sundays. The number of deaths can be used to solve the above problems (ref.3). There is no missing the number. In addition, the number of deaths is not affected by the closures of hospitals or the psychology of people. However, under the age of 70, the disease mortality decreases exponentially with age. According to the data, the mortality rate of COVID-19 is 25% in the 90s and over, 19% in the 80s, 7.5% in the 70s, 2.2% in the 60s, 0.51% in the 50s, 0.2% in the 40s, and 0.03% in the 30s (ref.4). Therefore, analysis of the death number can find older people with higher mortality rates, but not younger infected people with lower mortality rates. The percentage of infected people over the age of 70 is less than 10%. More seriously, it takes a long time from infection to death. Reference 3 reported that the change in the number of deaths was 23 days behind that of the confirmed cases. Reference 5 reported that the change in the number of infected people delayed about two weeks behind the actual infection. Therefore, the change in the number of deaths is information that is one and a half months behind the actual infection. In some cases, the epidemic ends before that. Therefore, analyzing the number of deaths does not help the timely evaluation of infectious disease countermeasures. We propose the PCR positive rate as the most reliable epidemic diagnosis for understanding the epidemic status by solving the above problems. The positive rate is a ratio of the positives to the number of the PCR tests. Examining the COVID-19 epidemic in Tokyo shows that the positive rate follows the epidemic accurately without being affected by medical institution closures or the psychology of people. By comparing with the change in the positive rate, we discuss that the asymmetry and the shallow p. 3 valleys in the number of confirmed cases were caused by people's psychology. From the fact that the positive rate did not go below 1-5% in the valleys of the epidemic, we discuss that many people are already infected and immune. The reasons for the positive rate following the number of positives accurately and for the observed fact that the value at the peak of the epidemic was lower than those reported in the test-negative design studies of influenza are attributed to the government's policy of finding as many patients as possible. Three possibilities are mentioned as the causes of the repeated COVID-19 epidemic in Japan; 1. a short lifetime of immunological memory cells, 2. quick mutation of the virus, 3. people getting sick due to sudden changes in climate show symptoms. All data used for analysis in this paper are publicly available. In both Tokyo and Osaka, data on the daily number of PCR tests and positives were obtained from the "Coronavirus Infectious Disease p. 4 seen in Fig. 1 (b) can be eliminated. The positive rate on Sunday was multiplied by 0.75 to reduce the weekly spikes in the curve of the positive rate. Figure 1 (c) shows the results of the day-of-week correction. There is a deep dent on July 22nd and 23rd in the change in the corrected number of positives. This dip is considered to be due to the special four consecutive holidays, in which two holidays were moved to coincide with the opening ceremony of the Tokyo 2020 Olympics. The big dent on August 9th will be due to summer vacation. These structures are not seen in the positive rate. As shown in Fig. 1 As shown in Fig.1 (c) , the August epidemic began in July, slowed in August, and peaked on August 11. Assuming that it takes two weeks from the actual infection to the PCR test results (ref. 5), the infection actually started in mid-June, slowed in mid-July, and peaked at the end of July. As mentioned above, the Tokyo Olympics started on July 23 and ended on August 8. One claim is that the Olympics have curbed the epidemic. However, this argument is not acceptable, as this epidemic is well fitted by the Gaussian theoretically expected for natural infections. Because the number of deaths is so small, the fluctuation of the data is large and the number of deaths is not suitable for detailed analysis of an epidemic. More seriously, the information is one month older than the change in the positives, so it is nearly useless for a quick evaluation of infectious disease countermeasures. p. 6 slightly heavier symptoms, the PCR test positive rate of these people may be high. In Japan, December 29th to January 3rd is the New Year holidays. People return to their hometowns and meet relatives. During this period, all schools are closed and many companies and most hospitals are also closed. The dip at the 1st week in Fig. 3 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 21, 2021. ; p. 7 to February was highly regional. The first epidemic in Japan last spring differs from subsequent epidemics in several points. First, as shown in Figure 5 confirmed cases decayed slower than the Gaussian shown by the green curve. In Osaka, the asymmetry was a little smaller but the number of confirmed cases was larger than the Gaussian in May. In detail, there is also a small asymmetry in this summer's epidemic. In Figure 1 (c), the number of positives in late August is slightly higher than that of the Gaussian, which is discussed later in the 4. Discussions. Third, the peak value of the positive rate was high. The peak value of the positive rate was less than 10% in last summer and this spring epidemics, 15% in this winter ( Fig. 4(b) ), and 22% this summer ( Fig. 1(c) ), but in the first epidemic shown in Figure 5 (a), the peak value of the positive rate was around 35%. In Osaka, the peak value of the positive rate in the first epidemic was 15% ( Fig. 5(b) ). As seen in Fig. 1(a) , there are five peaks in spring, summer in last year, winter, spring, and summer this year. In May last year after the first epidemic, the number of positives decreased to about 10 as seen in Fig. 5(a) , but after that, in the valleys of the second and later epidemic, confirmed cases were as large as 150, 200, and 250 in October, March, and June, respectively. The number of positives in the valley of the second and subsequent epidemics was comparable to or higher than the number of FIG.5: In the first epidemic, the peak of the number of the confirmed cases (black squares) was delayed by one week from the peak date of the positive rate (red squares) and the changing profile was asymmetry both in (a) Tokyo and(b) Osaka. All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in Similarly, the positive rate decreased to almost zero in May after the first epidemic as seen in Fig. 5(a) , but in the valleys of the second and later epidemic in October last year and March and June this year the positive rate decreased only to 4%. Also in Osaka, the positive rate decreased to 0% after the first epidemic as seen in Fig. 5(b) , but after that, the positive rate in the valleys of the epidemic was 1% to 3% as seen in Fig. 6 . The different behavior of the positive rate from the confirmed cases is that the values in the valleys are well smaller than the peak value in the first epidemic. When the population and microorganisms increase exponentially at the beginning, the rate of increase in the number of individuals decreases and converges to a steady value as the number approaches the capacity of the environment, and this phenomenon is described by the logistic equation Here, γ is the rate at which an infected person is quarantined or recovered, and S (t) is the number of uninfected persons at time t, given by the following equation. Both the logistic function and numerical solutions of K-M equations can be approximated by a Gaussian (ref. 2). Therefore, the epidemic of infectious diseases should be nearly symmetrical and approximated by a Gaussian. The above theory applies to an epidemic of a single source of a pathogen in a single community. All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 21, 2021. ; p. 9 The positive rate of this summer's epidemic in Tokyo in Fig. 1(c) can be fitted with a Gaussian. Therefore, we could understand that this epidemic was caused by a single source of a pathogen. However, the change in the number of positives deviated from the Gaussian after the peak. To make it easier to see, Fig. 7 shows an enlarged view of the change after the peak. The epidemic was peaked on August 12. The confirmed cases started to deviate upward from the Gaussian from August 19, one week after the peak and returned to the Gaussian on September 3. The number of positives was larger than the Gaussian only for two weeks. The deviated area is shown in orange. The increase in positives above the Gaussian can be due to psychological effects. Immediately after the peak, many were surprised by the surge in infected people, worried about themselves, and had their PCR tests. When the number of confirmed cases decreased to one-third of the peak, people were relieved and the number of PCR tests returned to normal. Of course, the number of positives was not false in this case as well. But the change in the number did not reflect the real epidemic. We get information on an epidemic from the shape of the change, and the shape of the change should be determined only by the epidemic, not by psychology. The percentage of people taking PCR tests can be any number but the essentially important thing is that the percentage should be always constant for knowing the real status of an epidemic. Fig.1 (c) after the peak of the summer epidemic. The number of positives deviated upward from the fitting Gaussian (orange part) for two weeks from Sep. 19 one week after the peak. All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in A psychological effect was also observed in the confirmed cases in the first epidemic last year April in Tokyo (Fig. 5(a) ). The change in the number of positives was asymmetry. The number of positives increased 10 times in about three weeks and peaked in mid-April. But it took five weeks for the number of positives to decrease to one-tenth of the peak value. This asymmetry can be explained as in the case of August this year discussed above. Asymmetry was noticed also in the first epidemic in Osaka. The number of the confirmed cases was larger than the Gaussian shown by the blue curve in May 2020 as seen in Fig. 5(b) . In the first epidemic last spring, the peak number of positives was one week behind the peak positive rate, with marked asymmetry as shown in Figure 5 . On the other hand, the asymmetry of this summer's epidemic seen in Figure 7 is small and can only be recognized by detailed analysis. This may mean that people were very afraid during the first epidemic, but that people are more reassured after experiencing some epidemics. The asymmetrical change in the number of infected people observed in Israel could be also attributable to a psychological effect. However, the number of positives increased greatly over the Gaussian in March after the peak, which can be a psychological effect. We know the positive rate generally expected in PCR tests for infectious diseases from researches on the test-negative design applied to influenza. From these researches, we know the PCR positive rate will be from 30% to 50% when patients suspected of a certain disease are PCR tested. From the values reported in the above papers, we understand the positive rate of the first COVID-19 epidemic in Tokyo was reasonable. However, the positive rate of 6% last summer, 15% at the beginning of this year, and 10% this summer are quite small. This is considered to reflect the policy of the Japanese government. In the researches mentioned above, the test-negative design for influenza targets people who develop influenza-like symptoms. However, the COVID-19 PCR tests are performed against the close contacts of already found positives in order to find as many infected individuals as possible. The positive rate is inevitably low because the test is done even if the patient is asymptomatic. The less likely an infected person is overlooked, the lower the positive rate. In Israel shown in Fig.8 , the positive rate at the peak of the epidemic last September was 14%, and the positive rate at the peak of other epidemics was 10%. Because the differences of the positive rate at the peaks and in the valleys in Tokyo of about 6% is very small compared to Israel, we can say that Japan's attitude to COVID-19 is more nervous than Israel. While the positive rate was over 30% in the first epidemic in Tokyo, it was about 10% in Israel. This might indicate that last spring the Israeli government was more cautious than Japan. After the first epidemic last spring, the positive rate decreased to almost zero % in Tokyo ( Fig. 5(a) ), Osaka (Fig. 5(b) ), and Israel (Fig. 8) . However, after the second epidemic and later, the positive rate in the valleys remained as large as 1 to 4%. Since the influence of psychological factors on the positive rate is negligible, the non-zero positive rate in the valleys implies that there are always coronavirus carriers among people even when COVID-19 is not in an epidemic. All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 21, 2021. ; p. 12 In the case of Okinawa, August when the test was conducted was after the first epidemic, so we can explain that the epidemic spread the virus among people. April 3rd to 7th when the tests were conducted at the hospital in Kobe was about a week before the peak of the number of positives, April 12th. But the peak date of the positive rate was April 5th. Then, the test in Kobe was performed only a few days before or at the peak of the epidemic. Therefore, it cannot be excluded that the epidemic spread the virus when Kobe hospital conducted the test for antibodies. In Tokyo (Fig. 5(a) ), Osaka (Fig. 5(b) ), and Israel (Fig. 8) In Israel, the positive rate was almost zero from April to June (Fig. 8 ). This can be the effect of the vaccine. However, to reach a conclusion, the time history of increased vaccination rates and decreased PCR positive rates needs to be analyzed in detail. Finally, we consider two important questions. If a doctor decides that a patient with symptoms similar to those of the target disease should undergo a PCR test, the positive rate will be almost 100% if the doctor is competent. Even if the doctor's ability is not very high, the positive rate will be 30% to 50%. In any case, the positive rate is almost constant regardless of the epidemic. All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 21, 2021. ; p. 13 Our hypothesis to explain the observed fact that changes in the positive rate of COVID-19 were in perfect agreement with changes in the number of confirmed cases is as follows. PCR tests to find COVID-19 patients are performed almost randomly, not just in patients with COVID-19-specific symptoms. If the test is random, the higher the number of patients in the epidemic, the more likely it is to find a patient, leading to a higher positive rate. Antibodies are produced in the body of infected persons and prevent the virus from entering again. Although the lifetime of antibodies is not so long, immunity is maintained for a long time when longlived immunological memory cells are produced (refs.21 -24) . Therefore, the epidemic will not repeat as long as the memory cells do not lose their ability. However, it is not uncommon for immunized infectious diseases to repeat epidemics. Rather, most infections are recurring. Common cold with multiple pathogens is repeated 1.5 times a year in adults (refs.25-28) . Most infectious diseases do not have sharp epidemic peaks, as seen in Fig. 3(a) . Influenza affecting 10% of Japanese people every year has a sharp peak in winter, but there are nonnegligible patients throughout the year. Infectious diseases develop without the invasion of external pathogens, which was evidenced without any doubt by the fact that Antarctic winterers who were isolated from the outside world for several months also caught colds (refs.29 and 30). From the above considerations, there are three possibilities as the cause of repeated COVID-19 epidemic; 1. a short lifetime of immunological memory cells, 2. the virus mutates frequently and the effect of the acquired immunity weakens, and 3. people develop the disease like a common cold. Examining the COVID-19 epidemic in Tokyo proved that the PCR test positive rate can be the An epidemic of infectious diseases of a single source of a pathogen in a single community is All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted September 21, 2021. ; p. 14 described theoretically by the K-M equation, and its numerical solution can be approximated by a Gaussian. In all five epidemics since the first epidemic in Spring last year in Tokyo, the changes in the positive rate were fitted quite well by Gaussians, which may imply all five epidemics can be an epidemic of a single source of a pathogen. While it was almost 0 % in the first valley after the first epidemic, the positive rate was as large as 1 to 4 % in the three valleys after the second epidemic, which was attributable to the widespread of the coronavirus among people. The peak values of the positive rate well lower than those reported for the test-negative design studies of influenza were attributed to the government's policy of finding as many patients as possible. The positive rate followed the positives closely not only in Tokyo but also in Osaka and Israel. This fact was also attributable to the policy. On the other hand, many asymmetric phenomena not fitted by a single Gaussian were observed in the number of confirmed cases. In all asymmetries, after the epidemic peak, the number of positives was higher than the Gaussian for fitting the rising part of the epidemic. These asymmetries were attributable to the psychology of people. Three possibilities were mentioned as the cause of the repeated COVID-19 epidemics in Japan; All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in In the first epidemic, the peak of the number of the confirmed cases (black square) was delayed by one week from the peak date of the positive rate (red square) and the changing profile was asymmetry both in (a) Tokyo and(b) Osaka. All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The number of confirmed cases in the valleys was high except after the first epidemic. All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in Understanding the present status and forecasting of COVID-19 in Wuhan. medRxiv preprint Israeli Ministry of Health, ‫בקרה‬ ‫לוח‬ -‫קורונה‬ (health Age structure of influenza patients, Number of patient reports download Visualizing the data: information on COVID-19 infections Interim Estimates of 2017-18 Seasonal Influenza Vaccine Effectiveness -United States Monitoring the efficacy of influenza vaccines in children: 2013/14-2015/16 Season Summary Ministry of Health, Labor and Welfare Science Research Results Database Monitoring the efficacy of influenza vaccines in children: 2016/17 Season. (in Japanese) Ministry of Health, Labor and Welfare Science Research Results Database Verhulst and the logistic equation (1838). pp 35-39, In: A Short History of Mathematical Population Dynamics A contribution to the mathematical theory of epidemics Antibodies were detected in 3% of 1,000 outpatients (Kobe City Hospital survey PCR tests on 2064 people in two days in Matsuyama, a downtown area of Okinawa A systematic review of antibody mediated immunity to coronaviruses: kinetics, correlates of protection, and association with severity Persistence and decay of human antibody responses to the receptor binding domain of SARS-CoV-2 spike protein in COVID-19 patients Persistence of serum and saliva antibody responses to SARS-CoV-2 spike antigens in COVID-19 patients Targets of T cell responses to SARS-CoV-2 coronavirus in humans with COVID-19 disease and unexposed individuals Acute respiratory illness in the community: frequency of illness and the agents involved Physical activity and immune function in elderly women Infectious-episodes-in-runners-before-and-after-the-LA-Marathon Psychological Stress and Susceptibility to the Common Cold There are deep dents in the 1st week and 18th weeks.(b) The deep dent in the 18th week due to the Golden Week in the change of the day-of-week corrected confirmed cases of COVID-19 (black squares) in Tokyo is not seen in the change in the PCR positive rate (red squares).All rights reserved. No reuse allowed without permission.perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint inThe copyright holder for this this version posted September 21, 2021.