key: cord-0804460-byp9heum authors: Yuan, Hsiang-Yu; Mao, Axiu; Han, Guiyuan; Yuan, Hsiangkuo; Pfeiffer, Dirk title: Effectiveness of quarantine measure on transmission dynamics of COVID-19 in Hong Kong date: 2020-04-11 journal: nan DOI: 10.1101/2020.04.09.20059006 sha: e5c3358b3235f360e8de5ace8908040480d29822 doc_id: 804460 cord_uid: byp9heum The rapid expansion of COVID-19 has caused a global pandemic. Although quarantine measures have been used widely, the critical steps among them to suppress the outbreak without a huge social-economic loss remain unknown. Hong Kong, unlike other regions in the world, had a massive number of travellers from Mainland China during the early expansion period, and yet the spread of virus has been relatively limited. Understanding the effect of control measures to reduce the transmission in Hong Kong can improve the control of the virus spreading. We have developed a susceptible-exposed-infectious-quarantined-recovered (SEIQR) meta-population model that can stratify the infections into imported and subsequent local infections, and therefore to obtain the control effects on transmissibility in a region with many imported cases. We fitted the model to both imported and local confirmed cases with symptom onset from 18 January to 29 February 2020 in Hong Kong with daily transportation data and the transmission dynamics from Wuhan and Mainland China. The model estimated that the reproductive number was dropped from 2.32 to 0.76 (95% CI, 0.66 to 0.86) after an infected case was estimated to be quarantined half day before the symptom onset, corresponding to the incubation time of 5.43 days (95% CI, 1.30-9.47). If the quarantine happened about one day after the onset, community spread would be likely to occur, indicated by the reproductive number larger than one. The results suggest that the early quarantine for a suspected case before the symptom onset is a key factor to suppress COVID-19. Introduction cases, the observed changes in numbers of cumulative cases are not totally due to those secondary infections 32 happened locally. Because current models cannot distinguish the imported and local infections, overestimation 33 of the reproductive number can be easily happened. In order to estimate the reproductive number and other epidemiological parameters of COVID-19 in Hong Kong, 36 here we developed a susceptible-exposed-infected-quarantined-recovered (SEIQR) meta-population model em-37 bedded with passenger data from Mainland China, that can stratify imported and local cases. We used Hong 38 Kong as an example to demonstrate that the model can successfully recapture the transmission dynamics of both 39 imported and local infections and estimate the reproductive number. Furthermore, the minimum timing and 40 intensity of quarantine to suppress the outbreak were estimated. 41 Data collection 43 We collected the date of symptom onset time for each daily newly infected case of COVID-19 from 18 January to 44 29 February 2020 in Hong Kong from the Centre for Health Protection, Government of the Hong Kong Special 45 Administrative [10] . Number of daily newly infected COVID-19 cases in Wuhan City and Mainland China 46 outside Wuhan from 16 January to 29 February 2020 were collected from the National Health Commission of 47 China [11] . Daily passenger data from Mainland China during the corresponding period were obtained from the 48 Hong Kong Immigration Department [12] . 49 SEIQR Meta-population model 50 The meta-population model was fitted first to the data from Wuhan and Mainland China (outside Wuhan). Using 51 the reconstructed transmission dynamics from source regions, the model was next fitted to the confirmed cases 52 with symptom onset in Hong Kong with transportation data. Assuming the newly emergence of COVID -19 53 causes an outbreak at location i, during the emergence, the changes of the numbers of infectious cases I j at a 54 different location j can be determined using a meta-population framework with a mobility matrix (contact mixing 55 at the population level) such that I j = I j imp + I j loc , where the subscripts imp and loc represent imported and 56 local cases and the number of I j imp is dependent on the mobility matrix. We developed an SEIQR model to 57 include dynamics of both imported and local cases at a target location (Hong Kong), and linked this model to 58 the meta-population framework: 5 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04.09.20059006 doi: medRxiv preprint where β is the transmission rate, τ is the latent periods, γ is the recovery rate, T qr is the time to quarantine after 67 being infectious and q is the recontact ratio of quarantined to unquarantined individuals. I imp , I loc , Q imp , Q loc 68 are the infectious imported cases, infectious local cases, infectious imported cases that are under quarantined 69 and infectious local cases that are under quarantined. Please see Table 1 and Table 2 Mainland China outside Wuhan (denoted as C). These numbers are determined by the daily passenger numbers 74 and incubation period: where M ji is the mobility rate from i to j, subscripts H, W , C indicates Hong Kong, Wuhan, Mainland China 77 (outside Wuhan), respectively. We used daily passenger data from the source regions divided by the population 78 size in the source regions to refer to M ji (Table S1 ). Among all the passengers from Mainland China, the 79 proportion of them coming from Wuhan to Hong Kong during the study period can be calculated using the 80 International Air Transport Association (IATA) database [13] . We estimated 2.92% of the total passenger from 81 of infected cases before symptom onset [14] and R pt is the reporting ratio. To obtain the number of imported cases, the model has to generate the transmission dynamics (I W and I C ) 88 at source regions and estimated the imported cases using transportation data. We used a simple SIR model to 89 6 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not peer-reviewed) The copyright holder for this preprint . Prior to parameter estimation, the transmission dynamics in Wuhan and non-Wuhan Mainland China were re-94 constructed using a modified SIR model. The resulting source dynamics were used as an initial condition to 95 seed imported cases for the target region ( Figure S1 and Figure The Gelman-Rubin convergence diagnostic was used and all the scores were less than 1.056 and near one, which 101 confirmed the convergence. Prior distributions for all the parameters were set to uniform distributions except the generation time T c and 103 the recontact ratio q. The prior of the generation time was assumed to be normally distributed with mean set 104 to be 7.95 days, the average from two previous studies [15, 16] . The standard deviation was 0.25. The mean 105 recontact ratio of being quarantined and not quarantined in a Gaussian prior was set to be 12% with a standard 106 deviation of 0.05. A recent study has estimated each individual can contact 12.5 persons on average during a 107 7 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint . https://doi.org/10.1101/2020.04.09.20059006 doi: medRxiv preprint day [17] . Assuming many self-quarantine individuals can likely contact to their household members, with a 108 possible expected number 1.5 persons, the mean recontact ratio of quarantined individuals to unquarantined in 109 the prior distribution can thus be determined as q = 1.5 12.5 . Likelihood of symptom onset The likelihood of observing onset dates of both confirmed imported and confirmed local cases in Hong Kong 113 were calculated based on Poisson distribution during MCMC. Newly detected infected cases are defined as the 114 newly infected cases with symptom onset that eventually became quarantined. We assumed all the confirmed 115 cases were quarantined. The daily newly detected imported cases with symptom onset was used as the expected 116 value of the Poisson distribution and can be derived as ∆I imp (σ)D, where ∆I imp = 1 τ E imp , and D is the detec-117 tion ratio, which was defined as the proportion of the number of quarantined imported cases to the total number 118 of infectious and quarantined cases. σ represents the pre-symptomatic transmission period, which produced a 119 delay of onset after an individual has been infected. The same approach can be used to determine the expected 120 value of the Poisson distribution for the detected local cases. Our meta-population model reproduced the COVID-19 transmission dynamics of both imported and local infec-129 tions in Hong Kong. The number of cumulative imported cases was increasing rapidly in Hong Kong after the 130 first imported case was detected, with onset day on 18 January 2020 until the end of Chinese New Year in early 131 February ( Figure 1A ). The risk of community spread was highlighted as the number of local cases crossed above 132 the imported cases. In order to understand the transmission dynamics of COVID-19 in Hong Kong, we devel-133 oped an SEIQR meta-population model that stratifies imported and local cases ( Figure 2 ). The model recaptured 134 the cumulative numbers with a crossover between the local and imported cases ( Figure 1B ) and transient dy-135 namics ( Figure 3 ). The predicted number of imported cases reached to a peak on 26 January ( Figure 3A ). These 136 imported cases immediately caused a wave of local infections. The number of daily newly detected local cases 137 reached to a peak around 2 February and decreased afterward ( Figure 3B ). period of approximately 5 days was reported [16, 19, 20] . We assumed all the infected persons can pass the border 146 before disease onset, which was defined as the incubation time. The results showed that the ratio can be low during the initial period but soon reached saturated values after 3 165 weeks both for imported and local cases ( Figure 6AB ). Generally the detection ratios of the imported cases were 166 higher than the local cases because the number of the imported cases were low. For local cases, 71%(46 − 90) of 167 which were detected, estimated by our model. One day delay of quarantine reduced about 10% of daily detection 168 ratio to 60%(39 − 74) ( Figure 6B ). Only 31%(20 − 39) of them could be detected or quarantined if quarantine 169 was delayed 6 days. The results showed that not only early quarantine can reduce reproductive number, but also 170 has a benefit on increasing overall detection ratio. Schema of susceptible-exposed-infected-quarantined-recovered meta population model. Imported cases arrive as exposed (E) status before disease onset in order to pass through the border. Imported cases then become infectious (I), quarantined (Q) or recovered (R) statuses. βη 1 Rpt M is the rate to produce imported cases, where η is a function to determine the probability of an ill passenger can pass the border (see Methods for the details). R pt is the reporting ratio in Mainland China and M is the mobility rate. Both imported and local cases are able to infect susceptible individuals (S) and cause local transmission while quarantined cases have a lower transmission rate depending on the recontact ratio (q), indicating the ratio of the contact rates of quanratined to unquarantined individuals. Epidemiological parameters β is the transmission rate, τ is the latent periods, γ is the recovery rate, T qr is the time to quarantine after being infectious. ∆I imp (σ)D represents the newly detected imported cases, where D is the detected ratio defined as the ratio of the number of quarantined imported cases to the total number of infectious and quarantined imported cases, and σ is the pre-symptomatic transmission period, indicating the delayed time of symptom onset after being infectious. Similarly, ∆I loc (σ)D represents the detected local cases. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint . 12 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint . https://doi.org/10.1101/2020.04.09.20059006 doi: medRxiv preprint . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint . https://doi.org/10.1101/2020.04.09.20059006 doi: medRxiv preprint . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint . Figure 6 Detection ratios of imported and local cases by time. (A) Detection ratios of imported cases. The ratios denote the proportion of daily newly cases with symptom onset that eventually become quarantined among all infectious cases. Blue, the detection ratio estimated using the posterior distribution of the time to quarantine, denoted as no delay. Red, the detection ratio estimated using the posterior distribution of the time to quarantine with one day delay. Green, the detection ratio estimated using the posterior distribution of the time to quarantine with six days delay. Shared areas are the 95% intervals. (B) Detection ratios of local cases. The ratios denote the proportion of daily newly cases with symptom onset that eventually become quarantined among all infectious cases. Same definition of colors are used as (A) but for local infections. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint . https://doi.org/10.1101/2020.04.09.20059006 doi: medRxiv preprint New Year festival in Hong Kong, we have identified the key aspects in containing the outbreak. This is the first 175 study to demonstrate that early time targeted quarantine measures significantly suppress the COVID-19 outbreak 176 and the proper timing of quarantine is feasible. Suppression of the outbreak during the study period is important 177 because global expansion occurred starting from this critical moment when initial travellers who carried the 178 diseases moved to different countries [21] [22] [23] [24] . Until now, how to suppress the outbreak of COVID-19 has been studied only in regions with many infections, 181 such as Wuhan or China [4, 21, 25, 26] . Although certain strict public health policies can suppress the outbreak, 182 these approaches can cause profound social and economic impacts, which may not be feasible by every country. 183 In contrast, our study illustrated that Hong Kong can be a good model to learn how to prevent the community 184 spread through quarantine before many other intensive control policies (such as transportation restriction and 185 closure of public facilities) are required. How to impose a large scale quarantine properly to suppress the outbreak remain largely unknown [6] . Our 188 results demonstrated that quarantine of suspected individuals before symptom onset, is critical to contain the 189 COVID-19 outbreak. Given that the incubation period was about 5 days and the confirmation of COVID -19 190 infection can often be delayed, to guarantee an early quarantine of all suspected cases before symptom onset is 191 a critical criterion to reduce the chance of community spread. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint . https://doi.org/10.1101/2020.04.09.20059006 doi: medRxiv preprint To obtain the number of imported cases, the model has to generate transmission dynamics in source regions is to seed the target region (Hong Kong). We modified an SIR to construct newly infected numbers that were close to the observed confirmed numbers in Wuhan and Mainland China (outside Wuhan). . Using 0 = 2.92, we can obtain = 0 = 0.3476 in Mainland China. We also assumed the recovery rate is same for both transmission dynamics in Mainland China and in Hong Kong. The effective reproductive number , was calculated using the next-generation matrix approach after obtaining the posterior distributions of model parameters. Following the same notation as in the study by Diekmann et al [2] . We obtained the transmission matrix and the transition . Elements in represents the average newly infected cases in exposed group (E) transmitted by a single infected individual in infectious or quarantined group (I), which can be calculated as or . can be calculated as the first eigenvector of −( −1 ) with the following formulas: . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04.09.20059006 doi: medRxiv preprint Figure S3 Posterior distributions of model parameters. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04.09.20059006 doi: medRxiv preprint Figure S4 Trajectories of MCMC output. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.04.09.20059006 doi: medRxiv preprint . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 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