An Epidemiological Model Considering Isolation to Predict COVID-19 Trends in Tokyo, Japan: Numerical Analysis

Abstract

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.

Infection spread simulation technology in a mixed state of multi variant viruses

“…The ATLM we have developed [12] 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. We denote the cumulative number of infected people by x as unknown, and daily infected people is by dx / dt .…”

“…The above methods do not have a time delay from infection to quarantine. We considered that the time required until isolated from infected is the important role of contribution in expanding infection, therefore we developed ATLM (Apparent Time Lag Model) with a delay until isolation time [12] . This model currently has an extended version with vaccine and lockdown effects [13] .…”

Novel deterministic epidemic model considering mass vaccination and lockdown against coronavirus disease 2019 spread in Israel: A numerical study

“…The effective reproductive number is defined as the average number of secondary cases by a primary case. ATLM defines the effective reproductive number Rt(t) in which the basic reproductive number is α(t)T [8] as In subsequent sections, we will compare predictions by Eqs. (3)-(7) with available data from Worldometer [9] and Our World in Data [10] and examine the present analysis method.…”

“…In view of these difficulties in the past literature, a deterministic approach different from SIR was attempted in the present study. Apparent Time Lag Model (ATLM) [8] was extended to include observed vaccine dose rate and NPI in Israel and the validity of the present model was demonstrated using publicly available data. This model is featured in small number of empirical constants most of which can be measured.…”

Infection spread simulation technology in a mixed state of multi variant viruses

“…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].…”