The effects of border control and quarantine measures on the spread of COVID-19

Abstract

The rapid expansion of coronavirus disease 2019 (COVID-19) has been observed in many parts of the world. Many newly reported cases of COVID-19 during early outbreak phases have been associated with travel history from an epidemic region (identified as imported cases). For those cases without travel history, the risk of wider spreads through community contact is even higher. However, most population models assume a homogeneous infected population without considering that the imported and secondary cases contracted by the imported cases can pose different risks to community spread. We have developed an "easy-to-use" mathematical framework extending from a meta-population model embedding city-to-city connections to stratify the dynamics of transmission waves caused by imported, secondary, and others from an outbreak source region when control measures are considered. Using the cumulative number of the secondary cases, we are able to determine the probability of community spread. Using the top 10 visiting cities from Wuhan in China as an example, we first demonstrated that the arrival time and the dynamics of the outbreaks at these cities can be successfully predicted under the reproduction number R₀ = 2.92 and incubation period τ = 5.2 days. Next, we showed that although control measures can gain extra 32.5 and 44.0 days in arrival time through an intensive border control measure and a shorter time to quarantine under a low R₀ (1.4), if the R₀ is higher (2.92), only 10 extra days can be gained for each of the same measures. This suggests the importance of lowering the incidence at source regions together with infectious disease control measures in susceptible regions. The study allows us to assess the effects of border control and quarantine measures on the emergence and global spread of COVID-19 in a fully connected world using the dynamics of the secondary cases.

Fig. 1

Statistics of airline passenger from Wuhan Tianhe International Airport and COVID-19 confirmed cases. (A) Number of airline passengers from Wuhan to top 10 visiting cities between 30 December, 2019 to 20 January, 2020. (B) Number of confirmed cases at top 10 visiting cities between 22 January to 28 January, 2020.

Fig. 2

COVID-19 outbreak spread from source to community transmission. (A) Outbreak progression from source to community spread. The imported cases arrive after passengers passed the border control. The secondary cases produced by the imported cases eventually cause the community outbreak. The community outbreak starts after t. (B) Mathematical model framework for COVID-19 estimates of secondary cases. I_i and I_j represent the numbers of infected cases in a source location i and a target location j respectively. M is the mobility rate and f(τ) is a function of incubation period that represent the percentage of infected cases that can pass the border (dashed line). T_g and T_qr are the generation time and time to quarantine respectively. β estimates the ratio $\frac{R_0}{T_g}$, where R₀ is the basic reproduction number.

Fig. 3

Outbreak potential estimated from the secondary cases contacted by imported cases. A higher R₀ = 2.92 scenario with incubation period τ = 5.2 days and time to quarantine T_qr = 2 days were used. (A) Number of cumulative secondary cases generated by imported cases. The secondary infections are listed among the top 10 visiting cities from Wuhan. ν = 8 is the critical threshold number; (B) Probability of outbreak emergence in different cities at mean arrival time (18 days).

Fig. 4

Observed number of confirmed cases and predicted number of imported and secondary cases. The predicted number of cases were adjusted by the reporting delay after using maximum likelihood estimation. The six cities that have the actual earliest arrival times are listed (four other remaining cities are given in Figure S5).

Fig. 5

Outbreak potential estimated from the secondary cases contacted by imported cases. A higher R₀ = 2.92 scenario with incubation period τ = 14 days and time to quarantine T_qr = 2 days were used. (A) Number of cumulative secondary cases generated by imported cases. The secondary infections are listed among the top 10 visiting cities from Wuhan. ν = 8 is the critical threshold number; (B) Probability of outbreak emergence in different cities at critical time (18 days).

Fig. 6

Assessment of border control and quarantine effects on outbreak arrivals. (A) Gain time of outbreak emergence by the rates of successful border control. The effects of border control on gain time under a low R₀ (1.4), mild R₀ (1.68), high R₀ (2.92) were plotted in blue, green, and red colors. (B) Gain time of outbreak emergence by time to quarantined. The effects of border control on gain time under a low R₀ (1.4), mild R₀ (1.68), high R₀ (2.92) were plotted using the same color codes as A. The passenger data of the top visiting city Beijing was used to generate the baseline arrival time. To get the gain time, the arrival time using different infectious disease control measures was calculated and was subtracted by the baseline arrival time.