Isolation Considered Epidemiological Model for the Prediction of COVID-19 Trend in Tokyo, Japan

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.

A Delay Differential Equation approach to model the COVID-19 pandemic

“…Thus, Shayak and coathours numerically investigated the simplest retarded logistic equation with time delay to model the spread of COVID-19 in a city and demonstrated that solution of the model is significantly sensitive to small changes in the parameter values (Shayak et al, 2020). In the same time, more conventional SEIR-based delay differential equation models were proposed to reproduce the COVID-19 dynamics in Germany, China, South Korea, India and Japan (Götz and Heidrich, 2020; Menendez, 2020; Sharma et al, 2021; Utamura et al, 2020) and to predict the epidemic dynamics in Italy and Spain when it was in its early stages. However, these models did not take into account asymptomatic carriers and non-testing subpopulations as well as the progression of the disease’s severity.…”

A delayed SEIQR epidemic model of COVID-19 in Tokyo

“…However, in their model, the patient that has passed an assumed period is quarantined once with an assumed probability, but if not quarantined, a chance of being quarantined is not left any longer. On the other hand, Utamura et al [17] developed a model named as "Apparent Time Lag Model (ATLM)" in that all the infectious patients are quarantined after passing an assumed period (14 days). Here, I have developed a new model introducing a compartment for quarantine possible infectious patients, where patients have a chance to be quarantined with a quarantine rate.…”

“…In their model, the patient that has passed an assumed period is quarantined with an assumed probability, but if not quarantined, a chance of being quarantined is not left any longer. On the other hand, Utamura et al [17] developed a model in that all the infectious patients are quarantined after passing an assumed period (14 days).…”