Effects of both input population and quarantine rates at different scenarios
The impact results of both the input population and quarantine rates on the COVID-19 disease are displayed in Fig. 8, 9 and STable 3. According to the results in “Effects of input population at different scenarios” and “Effects of quarantine rates at different scenarios” sections, the second outbreak of the disease are obtained in the scenarios with no or very weak quarantine strategy. Therefore, Figs. 8 and 9 only provide the COVID-19 disease variations of the scenarios with second outbreak, and the disease variations in other scenarios are not provided. STable 4 provides the results of all the scenarios.
Figure 8 Scenarios results of both input population and quarantine rates impacting on the cumuletive confirmed COVID-19 cases at four time points: (A) t1 = 10, (B) t1 = 20, (C) t1 = 28 and (D) t1 = 38 corresponding to Feb 6, 2020, Feb 16, 2020, Feb 24, 2020 and Mar 5, 2020.
Figure 9 Scenarios results of both input population and quarantine rates impacting on the cumuletive confirmed COVID-19 cases at four time points: (A) t1 = 10, (B) t1 = 20, (C) t1 = 28 and (D) t1 = 38 corresponding to Feb 6, 2020, Feb 16, 2020, Feb 24, 2020 and Mar 5,  2020.
For time point t 1  = 10, Sce 1: (p 2, A, q 1, q 2) = (1.5p 2  * , 1.5A  * , 0q 1  * , 0q 2  *), Sce 2: (p 2, A, q 1, q 2) = (1.5p 2  * , 2A  * , 0q 1  * , 0q 2  *), Sce 7: (p 2, A, q 1, q 2) = (2p 2  * , 1.5A  * , 0q 1  * , 0q 2  *) and Sce 8: (p 2, A, q 1, q 2) = (2p 2  * , 2A  * , 0q 1  * , 0q 2  *) have the MVCCC larger than 10 million at 328, 313, 327 and 312 days (Fig. 8A, STable 3). In fact, they have the two outbreaks of the disease with the confirmed cases having the first peak value as the baseline result at Feb 10, 2020 and the second peak values larger than 1 million at 142 days, 132 days, 141 days and 130 days for Sce1, Sce 2, Sce 7 and Sce 8, respectively (Fig. 9A, STable 3). The magnified figure in the period of Jan 27, 2020-Apr 26, 2020 clearly displays the second outbreak of this disease (Fig. 9A). Moreover, the weak changes of the four scenarios in the quarantine rates or around the time point t 1  = 10, the second outbreak also resulted in the second outbreak of the disease.
If the control measures employed as the four scenarios after the other three time points t 1  = 20, t 1  = 28, and t 1  = 38, the MVCCC are rapidly decreased with still larger than the baseline results, and the DDE are prolonged except the Sce 2 and Sce 8 of t 1  = 28, and t 1  = 38 (STable 4).
For the other scenarios: Sce 3-Sce 6 and Sce 9-Sce 12 of the four time points, the DDE become smaller than the baseline result due to the larger input population and more exposed individuals. Moreover, the weaker quarantine rates together with the more input population resulted in the more infected individuals and increased the MVCCC (STable 4).