Background COVID-19 currently poses a global public health threat. Although Tokyo, Japan, is no exception to this, it was initially affected by only a small-level epidemic. Nevertheless, medical collapse nearly happened since no predictive methods were available to assess infection counts. A standard susceptible-infectious-removed (SIR) epidemiological model has been widely used, but its applicability is limited often to the early phase of an epidemic in the case of a large collective population. A full numerical simulation of the entire period from beginning until end would be helpful for understanding COVID-19 trends in (separate) counts of inpatient and infectious cases and can also aid the preparation of hospital beds and development of quarantine strategies. Objective This study aimed to develop an epidemiological model that considers the isolation period to simulate a comprehensive trend of the initial epidemic in Tokyo that yields separate counts of inpatient and infectious cases. It was also intended to induce important corollaries of governing equations (ie, effective reproductive number) and equations for the final count. Methods Time-series data related to SARS-CoV-2 from February 28 to May 23, 2020, from Tokyo and antibody testing conducted by the Japanese government were adopted for this study. A novel epidemiological model based on a discrete delay differential equation (apparent time-lag model [ATLM]) was introduced. The model can predict trends in inpatient and infectious cases in the field. Various data such as daily new confirmed cases, cumulative infections, inpatients, and PCR (polymerase chain reaction) test positivity ratios were used to verify the model. This approach also derived an alternative formulation equivalent to the standard SIR model. Results In a typical parameter setting, the present ATLM provided 20% less infectious cases in the field compared to the standard SIR model prediction owing to isolation. The basic reproductive number was inferred as 2.30 under the condition that the time lag T from infection to detection and isolation is 14 days. Based on this, an adequate vaccine ratio to avoid an outbreak was evaluated for 57% of the population. We assessed the date (May 23) that the government declared a rescission of the state of emergency. Taking into consideration the number of infectious cases in the field, a date of 1 week later (May 30) would have been most effective. Furthermore, simulation results with a shorter time lag of T=7 and a larger transmission rate of α=1.43α0 suggest that infections at large should reduce by half and inpatient numbers should be similar to those of the first wave of COVID-19. Conclusions A novel mathematical model was proposed and examined using SARS-CoV-2 data for Tokyo. The simulation agreed with data from the beginning of the pandemic. Shortening the period from infection to hospitalization is effective against outbreaks without rigorous public health interventions and control.

<abstract> <p>ATLM (Apparent Time Lag Model) was extended to simulate the spread of infection in a mixed state of the variant virus and original wild type. 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 d strain (L452R) virus, while the increase by a strain (N501Y) virus will be suppressed. (3) It is anticipated that the infection will spread during the Olympic Games. (4) When variant viruses compete, 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 the vaccine.</p> </abstract>

Background: Coronavirus Disease 2019 (COVID19) currently poses a global public health threat. Although no exception, Tokyo, Japan was affected at first by only a small epidemic. Medical collapse nevertheless nearly happened because no predictive method existed for counting patients. A standard SIR epidemiological model and its derivatives predict susceptible, infectious, and removed (recovered/deaths) cases but ignore isolation of confirmed cases. Predicting COVID19 trends with hospitalized and infectious people in field separately is important to prepare beds and develop quarantine strategies. Methods: Time-series COVID19 data from February 28 to May 23, 2020 in Tokyo were adopted for this study. A novel epidemiological model based on delay differential equation was proposed. The model can evaluate patients in hospitals and infectious cases in the field. Various data such as daily new cases, cumulative infections, patients in hospital, and PCR test positivity ratios were used to examine the model. This approach derived an alternative formulation equivalent to the standard SIR model. Its results were compared quantitatively with those of the present isolation model. Results: The basic reproductive number, inferred as 2.30, is a dimensionless parameter composed of modeling parameters. Effects of intervention to mitigate the epidemic spread were assessed a posteriori. An exit policy of how and when to release a statement of emergency was also assessed using the model. Furthermore, results suggest that the rapid isolation of infectious cases has a large potential to effectively mitigate the spread of infection and restores social and economic activities safely. Conclusions: A novel mathematical model was proposed and examined using COVID19 data for Tokyo. Results show that shortening the period from infection to hospitalization is effective against outbreak without rigorous public health intervention and control. Faster and precise case cluster detection and wider and quicker introduction of testing measures are strongly recommended.

Why public health intervention by Israel government against COVID-19 spread has been successful while the most countries in the world is still coping with it? To give the answer, a simple numerical epidemic model is prepared to simulate an entire trend of various infection related variables considering vaccination campaign and simultaneous lockdown. The model is an extension of the deterministic physical model ATLM previously published by the authors that aims to predict an entire trend of variables in a single epidemic. The time series data of both vaccine dose ratio and lockdown period are employed in the model. Predictions have been compared with observed data in terms of daily new cases, isolated people, infectious at large and effective reproductive number and the model is verified. Moreover, parameter survey calculations for several scenarios have clarified a synergy effect of vaccination and lockdown have existed. In particular, it is suggested the key element of Israel success lies in a high dose rate of vaccination that avoids the onset of the rebound of daily new cases on the rescission of the lockdown.