A delayed SEIQR epidemic model of COVID-19 in Tokyo

Abstract

The rapid expansion of COVID-19 has caused a global pandemic. In order to avoid excessive restriction to the social activity, a good strategy of quarantine is needed. Several epidemic models with a quarantine compartment such as susceptible-exposed-infectious-quarantined-removed (SEIQR) model have been applied. However, in the actual situation, the infection test and quarantine is often delayed from the beginning of the infectious stage. This article presents a delayed SEIQR model to analyze the effect of the delay of quarantine, and to suggest a guideline for the measure. The latency period (compartment E) was assumed to be 3 days, and the start of quarantine action was assumed to be delayed by 4 to 10 days from infection. The actual PCR test-positive number data from March 10th to July 18th in 2020 was analyzed to estimate a transmission rate and the reproduction number. The area where the infection expansion is restrained was displayed in the two parameter space (transmission rate and quarantine rate) for several possible lengths of the delay of quarantine. As a result, it was shown to be very hard to restrain the expansion of infection only by a simple quarantine action retaining the delay. As a short term measure, it was found to be necessary to reduce the transmission rate through some kind of restriction of social activity, but as a long term measure, it was found to be possible to maintain the social activity by shortening the delay of quarantine through expanding the infection test system to find earlier stage patients, including asymptomatic infectious patients. In order to shed light to this conclusion from a different viewpoint, this model was applied in another case that an additional quarantine was taken into account before the delay. The result was shown to have a similar effect as that of the shortening of the delay.