key: cord-0296423-jecn4n34 authors: Koizumi, M.; Utamura, M.; Kirikami, S. title: Infection spread simulation technology in a mixed state of multi valiant viruses date: 2021-07-03 journal: nan DOI: 10.1101/2021.06.28.21259679 sha: dc8689b35031ffc573abf0b410b0b943ae059691 doc_id: 296423 cord_uid: jecn4n34 ATLM was extended to simulate the spread of infection in a mixed state of mutant virus and conventional virus. It is applied to the 4th wave of infection spread in Tokyo, and (1) the 4th wave bottoms out near the end of the state of emergency, and the number of infected people increases again. (2) The rate of increase will be mainly by L452R virus, while the increase by N501Y virus will be suppressed. (3) It is anticipated that the infection will spread during the Olympic Games. (4) When mutant virus competes, the infection of highly infectious virus rises sharply while the infection by weakly infectious ones has converged. (5) It is effective as an infection control measure to find an infected person early and shorten the period from infection to quarantine by PCR test or antigen test as a measure other than vaccine. incorporates these effects into the coefficients is also performed at SEIR [3] . B Ritton et al. applied improved SEIR to spread infection under the case of non-uniform population structure [4] . On the other hand, ABM (Agent Based Model) has been developed [5] [6] [7] [8] [9] . This technology is a probabilistic method, and unlike the deterministic methods such as SIR and SEIR, it is a method that assumes various behaviors of a person and calculates the infection probability, and it takes a considerable amount of calculation time. The above methods do not have a time delay from infection to quarantine. We considered that the time required until isolated from infected is important role of contribution in expanding infection, therefore we developed ATLM (Apparent Time Lag Model) with delay until isolation time [10] . This model currently has an extended version with vaccine and lockdown effects [11] . The infectivity of mutant viruses has already been reported [12] and the spread of the virus has been simulated. However, there are few knowledges about infection patterns by multi variant viruses and it has not been understood yet how each mutation virus to spread or to contribute, also how strong mutation virus to become mainstream spread. In this report, we have expanded it to handle mutant viruses. If there is only one type of infectivity, several proposals such as SIR and SEIR have been proposed. The ATLM we have developed uses the following equation, which takes into account the time delay from infection to quarantine and the time delay from infection to loss of infectivity. where, x: cumulative number of infected persons, T: number of days from infection to quarantine, μ(t): vaccination rate, α: infection coefficient, : ratio of asymptomatic persons, S is the number of days from infection to extinction of infectivity. M indicates the sensitive population. ρ (t) is the rate of decrease in the infection coefficient due to the restriction of human flow due to lockdown. Equation (3) represents the decrease in the target population due to vaccination. To extend the above equation for handling the modified viruses, the following assumptions are taken into account. (1) Infected persons are infected with only one type of virus, and there is no simultaneous infection. (2) Patients who have been infected with one mutant virus in the past are not infected with other mutant virus. (3) The infection rates between viruses are independent of each other and do not interfere with each other. (4) The effect of the vaccine is the same for each mutant will. (5) The time until the onset and the time until the infectivity disappears are the same. Above assumptions the group, i species modified viruses formula spread by is as follows. Equation (5) is a limitation that comes from assumptions (1) and (2) . That is, it is shown that the infected target is the same susceptible population even if the mutant species are different. The analytical solution of the differential equation of Eq. (4) is unknown. Therefore, to solve the above equation, the 4th-order Runge-Kutta method was used for numerical integration. In equation (4) . t-T and t-S value point of xi in the calculation time t, is computed, especially no problem on accuracy. However, the calculation start time of the point is tricky because it is unknown. Therefore, the initial value is given a sufficiently small value compared to M0. Next, it should be noted that, when X(t) is increased, too close to M(t). Especially when the vaccination rate becomes high, X(t) >M(t) may occur, in which case the solution oscillates and becomes unstable. Here, if X(t)/M(t)>1, we set the righthand side of equation (4) (which 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 this version posted July 3, 2021. ; https://doi.org/10.1101/2021.06.28.21259679 doi: medRxiv preprint conventional ones [13] . Thus, when infectivity of virus that are currently prevalent is assumed to be unity, taking the ratio of the two, 1.35 becomes a factor. Some people say that this ratio is about 1.2, and many discussions have not yet been finalized. So, we assume to be 1.35 is the factor of L452R to N501Y virus. Table 1 shows calculation conditions. The initial value was determined so as to satisfy the above conditions. See wave. Figure 2 shows the number of quarantined persons, including home medical treatment and hotel medical treatment. It is said that 80% of the infected person is mild person are not in hospital, then remaining of 20% are in the hospital. Therefore, at the peak more 11000 people has been quarantined and about 2200 people is considered in the hospital. According to the data of Tokyo [14] at the time of the fourth wave peak All rights reserved. No reuse allowed without permission. (which 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 this version posted July 3, 2021. ; https://doi.org/10.1101/2021.06.28.21259679 doi: medRxiv preprint about 2400 patients are counted, then the results are consistent with the actual data. Figure 3 displays number of infected people during infection until isolation in a community. The higher this number, the higher the probability of having the next infected person. Figure 4 shows the average infection coefficient of the mutant virus, and as the infection progresses, the average value becomes closer to the infection coefficient of L452R. It shows that the L452R is becoming dominant. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Figure 8 shows a ratio of infected persons by L452R and N501Y. The number of infected people by L452R increases from the emergency situation declared the All rights reserved. No reuse allowed without permission. (which 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 this version posted July 3, 2021. ; https://doi.org/10.1101/2021.06.28.21259679 doi: medRxiv preprint end and becomes dominant after the point of 2021/7/6 (128 infected people number in days). In addition, from these figures, it can be seen that the infection by the highly infectious L452R rises sharply at the stage when the infection of N501Y has converged and bottomed out. As described above, this analysis also showed that the one with stronger infectivity became dominant when the infection spread. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (2) Measure 1: In the case of extending the state of emergency to 6/30 (Case 2) Figure 9 shows the transition of infected persons when the state of emergency is extended to 6/30. Peak of infected persons 100 decreases as people, but the big improvement of the infection situation is not observed. Therefore, the extension until 6/30 has no effect on suppressing infection. All rights reserved. No reuse allowed without permission. (which 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 this version posted July 3, 2021. ; https://doi.org/10.1101/2021.06.28.21259679 doi: medRxiv preprint This measure is not effective unless as many people as possible participate. It is good if you know that you will be infected, but usually you do not know, so you need to have many people check it regularly. For that purpose, many people can participate by issuing a negative certificate for a limited time (up to one week) in the test and confirming it at restaurants and event venues. In this way, it is possible to shorten the period from infection to isolation for two days or one day. In this study, this period is set to 14 days due to the consistency of the data, but it is estimated to be about 7 days in reality. Then, one actual day short is equivalent to two days of the study. We set the period to 12 days. Considering five days as preparation period after the end of emergency, the implementation date was set to 6/25. The results are shown in Fig. 10 . As shown in the figure, the spread of infection after the peak of the 4th wave is suppressed to about 600 people. Searching for infected people early and shortening the infection period in this way is the most effective method other than vaccines as an infection control measure. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. In Fig. 11 , the infection status of each cases are plotted together. The horizontal axis is the date from 2021/3/1. The blue line shows the infection status in Tokyo on a 7-day average [14] . From this figure, it can be seen that Case 3 suppresses the spread of infection most and is effective. (which 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 this version posted July 3, 2021. ; https://doi.org/10.1101/2021.06.28.21259679 doi: medRxiv preprint We have extended the ATLM which has been developed to simulate the status of infection with various mutant viruses. The developed model was applied to the 4th wave of Tokyo and the following results were obtained. (1) The fourth wave will bottom out near the end of the state of emergency, and the number of infected people will increase again. (2) The rate of increase will be mainly by L452R virus, while the increase in N501Y virus will be suppressed. (3) It is anticipated that the infection will spread during the Olympic Games. We used time-series data of COVID-19 for March 1 through June 10, 2021 in Tokyo [14] . Here, ) (t x : cumulative infections, T: delay time from infection to quarantine, u: the step function. Since daily new cases varies significantly, integration is used to smooth them. The intervals are used as those of interest. The following equation is obtained from the integration of (A-1) in the interval ] , Normally, 1 t T  . For this reason, we set the step function u = 1. The condition (A-5) is sufficient for M and α to be positive. The case of Tokyo The source is from the following. (which 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 this version posted July 3, 2021. ; https://doi.org/10.1101/2021.06.28.21259679 doi: medRxiv preprint In the above, the calculation of the first approximations of M and α is shown by taking the case of Tokyo. These must be so tuned that they are consistent with the other measurements. All rights reserved. No reuse allowed without permission. (which 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 this version posted July 3, 2021. ; https://doi.org/10.1101/2021.06.28.21259679 doi: medRxiv preprint The Joint Impact of COVID-19 Vaccination and Non-Pharmaceutical Interventions on Infections, Hospitalizations, and Mortality: An Agent-Based Simulation | medRxiv doi Possible effects of mixed prevention strategy for COVID-19 epidemic: massive testing, quarantine and social distancing A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2 An agent-based model to evaluate the COVID-19 transmission risks in facilities Adapting French COVID-19 vaccination campaign duration to variant dissemination | medRxiv doi Agent-Based Simulation of Covid-19 Vaccination Policies in CovidSIMVL | medRxiv doi The Impact of Vaccination to Control COVID-19 Burden in the United States: A Simulation Modeling Approach | medRxiv doi High-Resolution Agent-Based Modeling of COVID-19 Spreading in a Small Town --Truszkowska --2021 --Advanced Theory and Simulations An Epidemiological Model Considering Isolation to Predict COVID-19 Trends in Tokyo, Japan: Numerical Analysis. JMIR Public Health Surveill A novel deterministic epidemic model considering mass vaccination and lockdown against Covid-19 spread in Israel: Numerical study Updates on COVID-19 in Tokyo | Tokyo Metropolitan Government COVID-19Information Website This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors. The authors declare that they have no conflict of interest related to this report or the study it describes. MK is the former researcher of Hitachi Ltd., MU is the former professor of Tokyo Institute of Technology and SK is the former engineer of Hitachi Ltd. Usually, the following inequality holds in the range of monotonously increasing . ) ( dt t dx