When to lift the lockdown in Hubei province during COVID-19 epidemic? An insight from a patch model and multiple source data

Abstract

After diagnosed in Wuhan, COVID-19 spread quickly in mainland China. Though the epidemic in regions outside Hubei in mainland China has maintained a degree of control, evaluating the effectiveness and timeliness of intervention strategies, and predicting the transmission risk of work resumption as well as lifting the lockdown in Hubei province remain urgent. A patch model reflecting the mobility of population between Hubei and regions outside Hubei is formulated, and parameterized based on multiple source data for Hubei and regions outside Hubei. The effective reproduction numbers for Hubei and regions outside Hubei are estimated as 3.59 and 3.26 before Jan 23rd, 2020, but decrease quickly since then and drop below 1 after Jan 31st and Jan 28th, 2020. It is predicted that the new infections in Hubei province will decrease to very low level in mid-March, and the final size is estimated to be about 68,500 cases. The simulations reveal that contact rate after work resumption or lifting the lockdown in Hubei plays a critical role in affecting the epidemic. If the contact rate could be kept at a relatively low level, work resumption starting as early as on March 2nd in Hubei province may not induce the secondary outbreak, and the daily new infectious cases can be controlled at a low level if the lockdown in Hubei is liftted after March 9th, otherwise both work resumption and lifting the lockdown in Hubei should be postponed.

Keywords: COVID-19; Effective reproduction number; Lift the lockdown; Patch model; Work Resumption.

Fig. 1

The flow chart of the model. The red dotted line from suspected and infected class to confirmed class in Hubei patch denotes the extra confirmation rate after Feb 8th, 2020 in Hubei province.

Fig. 2

Daily data for Hubei and regions outside Hubei. (A) new reported cases, (B) new deaths, (C) existing suspected cases in Hubei province, (D) new suspected cases.

Fig. 3

Mobility indices from and to Wuhan city. (A) the mobility index. (B) the proportion of mobility within Hubei province.

Fig. 4

Data fitting results. (A) daily new reported cases in Hubei province, (B) daily new deaths in Hubei province, (C) existing suspected cases in Hubei province, (D) daily new reported cases in regions outside Hubei, (E) daily new deaths in regions outside Hubei, (F) daily new suspected cases in mainland China. The orange stars illustrate the real data, the blue curves show the model predicting results.

Fig. 5

The effective reproduction number in Hubei and regions outside Hubei.

Fig. 6

Comparison between model prediction with real reported data. (A) cumulative number of cases in Hubei province, (B) cumulative number of cases in regions outside Hubei province. The orange stars illustrate the real data, the blue curves show the model predicting results.

Fig. 7

Effect of work resumption time on the epidemic in Hubei province. (A) shows the result of no work resumption. (B)–(D) show the effect of work resumption. After work resumption, it is assumed that the contact rate becomes (B) 5%, (C) 10%, (D) 20% of the level before Jan 23, 2020. The work resumption time are Mar 2, Mar 9, Mar 16 and Mar 23, which are illustrated in black, cyan, red and green curve, respectively.

Fig. 8

Effect of work resumption time on the epidemic in regions outside Hubei. (A) shows the result of no work resumption. (B)–(D) show the effect of work resumption. After work resumption, it is assumed that the contact rate becomes (B) 5%, (C) 10%, (D) 20% of the level before Jan 23, 2020. The work resumption time are Mar 2, Mar 9, Mar 16 and Mar 23, which are illustrated in black, cyan, red and green curve, respectively.

Fig. 9

Effect of lifting the lockdown in Hubei on the epidemic in regions outside Hubei. (A) shows the results of continuing lockdown measure. (B)–(D) show the results for lifting the lockdown in Hubei. After lifting the lockdown in Hubei, it is assumed that the contact rate becomes (B) 5%, (C) 10%, (D) 20% of the level before Jan 23, 2020. The time of lifting the lockdown in Hubei are Mar 2, Mar 9, Mar 16 and Mar 23, which are illustrated in black, cyan, red and green curve, respectively.

Fig. 10

Sensitivity analysis. (A) variations of the logarithm cumulative number of confirmed cases in Hubei province. (B) variations of the logarithm cumulative number of confirmed cases in regions outside Hubei. (C) Partial Rank Correlation Coefficients (PRCC) for the dependence of cumulative number of cases in April 1st in Hubei province on each parameter. (D) Partial Rank Correlation Coefficients (PRCC) for the dependence of cumulative number of cases in April 1st in regions outside Hubei on each parameter.