Evaluation of the effect of the state of emergency for the first wave of COVID-19 in Japan

Abstract

In this paper, we evaluate the effect of the state of emergency for the first wave of COVID-19 in Japan, 2020 from the viewpoint of mathematical modelling. In Japan, it was announced during the period of the state of emergency from April 7 to May 25, 2020 that the 80% reduction of the contact rate is needed to control the outbreak. By numerical simulation, we show that the reduction rate seems to have reached up to 86%. Moreover, we estimate the control reproduction number $R_c$ during the period of the state of emergency as $R_c=0.36$ (95%CI, 0.34-0.39), and show that the effective reproduction number $R_e$ after the lifting of the state of emergency could be greater than 1. This result suggests us that the second wave of COVID-19 in Japan could possibly occur if any effective intervention will not be taken again.

Keywords: Basic reproduction number; COVID-19; SEIR epidemic model; State of emergency.

Fig. 1

Daily number of newly reported cases of COVID-19 in Japan from January 15 to June 30, 2020. The start and end of the state of emergency (SOE) are on April 7 and May 25, 2020, respectively.

Fig. 2

Comparison of the actual data of COVID-19 in Japan, 2020 and the predicted epidemic curve for ${\mathcal{R}}_0=2.6$ (95%CI, 2.4–2.8), which was estimated in (Kuniya, 2020) using the early data (from January 15 to February 29, 2020).

Fig. 3

Transfer diagram for the SEIR model.

Fig. 4

The weighted least square function $L\left(k\right)$ versus $0<k<1$.

Fig. 5

Comparison of the daily number of newly reported cases of COVID-19 in Japan, 2020 and the estimated epidemic curve with model (1) for $t\in T_1$ and model (2) for $t\in T_2$ ($k^{\text{∗}}=0.14$).

Fig. 6

(a) The weighted least square function $L_2\left(k_2\right)$ versus $0<k_2<1$; (b) Comparison of the daily number of newly reported cases of COVID-19 in Japan, 2020 and the estimated epidemic curve with model (1) for $t\in T_1$, model (2) for $t\in T_2$ and model (3) for $t\in T_3\cup \left(\mathrm{167,365}\right]$ ($k^{\text{∗}}=0.14$ and $k_2^{\text{∗}}=0.45$).