The Effects of Border Control and Quarantine Measures on Global Spread of COVID-19

Abstract

The rapid expansion of coronavirus (COVID-19) has been observed in many parts of the world. Many newly reported cases of this new coronavirus have been associated with travel history from an epidemic region (identified as imported cases). However, for those cases in which source remains unknown, the risk of wider spreads through community contact is even higher. To prevent global spread, it is essential to block potential coronavirus carriers to come in to a susceptible region and to prevent local transmission. Although meta-population model has been used widely to evaluate the effect of control measures against disease spreading, most of the studies assume a homogeneous infected population without considering that the secondary cases contracted by the imported cases have a direct link to community spread.

We have developed an “easy-to-use" mathematical framework, extending from an SIR meta-population model embedding city-to-city connections to obtain the dynamics of transmission waves (that is, primary (imported), secondary, tertiary cases and so on) from an outbreak source region to different susceptible regions using four basic epidemiological parameters, R₀, τ, T_g, T_qr, i.e., the basic reproductive number, incubation time (used for latent period), generation time, and time to quarantine, respectively, along with a mobility matrix M to represent the number of daily passengers. In our framework, the probability of outbreak emergence was defined by the number of secondary cases and a predefined threshold number.

We first demonstrated that the reporting delay can be successfully predicted as 10.52 (10.27-10.78) days. Next, the arrival time (when the probability of outbreak emergence is larger than 50%) and the dynamics of the outbreaks in other cities in Mainland China can be predicted at the end of January 2020 using air travel frequency data before Wuhan lockdown under R₀ =2.92 and τ =5.2 days. Finally, we assessed the effects of border control and quarantine measures on outbreak arrival time with different R₀ settings using passenger number to Beijing as baseline. The results showed that although control measures can gain extra 32.5 and 44.0 days in arrival time through high intensive border control (which reduces 90% of passengers) and shorter time to quarantine of suspected cases (1 day after infectious state starts), respectively, 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 the source together with the infectious disease control measures in other countries. The study allows us to assess the effects of border control and quarantine measures on virus spread and arrival time of outbreak emergence in a fully connected world using secondary cases.

Funding Statement: The authors also acknowledge the support from the grants funded by City University of Hong Kong [#7200573 and #9610416] and the ministry of Science and Technology in Taiwan [MOST 108-2638-H-002-002-MY2].

Declaration of Interests: All authors declare no competing interests.

Keywords: COVID-19; Global spread; Infectious Disease Control; Meta-population model; Outbreak arrival time; SIR model