The effectiveness of full and partial travel bans against COVID-19 spread in Australia for travellers from China during and after the epidemic peak in China

Abstract Background Australia implemented a travel ban on China on February 1st 2020, while COVID-19 was largely localised to China. We modelled three scenarios to test the impact of travel bans on epidemic control. Scenario one was no ban, scenario two and three were the current ban followed by a full or partial lifting (allow over 100 000 university students to enter Australia, but not tourists) from the 8th of March 2020. Methods We used disease incidence data from China and air travel passenger movements between China and Australia during and after the epidemic peak in China, derived from incoming passenger arrival cards. We used the estimated incidence of disease in China, using data on expected proportion of under-ascertainment of cases, and an age specific deterministic model to model the epidemic in each scenario. Results The modelled epidemic with the full ban fitted the observed incidence of cases well, predicting 57 cases on March 6th in Australia, compared to 66 observed on this date, however we did not account for imported cases from other countries. The modelled impact without a travel ban results in more than 2000 cases and about 400 deaths, if the epidemic remained localised to China and no importations from other countries occurred. The full travel ban reduced cases by about 86%, while the impact of a partial lifting of the ban is minimal, and may be a policy option. Conclusions Travel restrictions were highly effective for containing the COVID-19 epidemic in Australia during the epidemic peak in China and averted a much larger epidemic at a time when COVID-19 was largely localised to China. This research demonstrates the effectiveness of travel bans applied to countries with high disease incidence. This research can inform decisions on placing or lifting travel bans as a control measure for the COVID-19 epidemic.

3 effectiveness of travel bans applied to countries with high disease incidence. This research can inform decisions on placing or lifting travel bans as a control measure for the  epidemic.

Introduction
In response to the epidemic of COVID-19, 1 Australia implemented a travel ban from China on February 1 st 2020, adding Iran and then South Korea and Italy to the ban on February 29 th , March 5 th and 10 th respectively. In addition, Australians evacuated from Wuhan and from the Diamond Princess cruise ship were quarantined for two weeks in dedicated quarantine facilities. The ban on travel from China has been periodically reviewed, with lifting of restrictions announced on February 23 rd for high school students, who number less than 800.
In contrast, over 120000 university students are unable to enter Australia to commence or resume their studies, and a booming tourism industry has ceased.
Non-pharmaceutical interventions measures like social distancing and quarantine are effective public health tools to control epidemic diseases 2 , and Australia successfully delayed the introduction of the 1918 influenza A H1N1 pandemic by 1 year and reduced the total mortality compared to other countries 3 . However, evidence on the effectiveness of travel bans in containing the global spread of emerging infectious diseases is still limited 4 and they are not sustainable indefinitely. Therefore, a careful risk analysis needs to be done comparing the health and economic consequences implementing travel bans for the control of COVID-19 for alternative scenarios of increasing and decreasing disease incidence. The epidemic in China peaked on February 5 th and has declined since 5 We aimed to estimate the impact of the implementation of the travel ban on China from February 1 st , 2020 on the epidemic trajectory in Australia, as well as the impact of lifting the ban completely or partially from the 8 of March, when disease incidence was waning in China.

Methods:
Three scenarios were considered.  instituted in this analysis, or lifted, it was assumed that international students unable to enter Australia would return to Australia following the lifting of the ban, 60% in the rest of March and the remaining 40% over the month of April. However, tourists not able to travel during a travel ban were not assumed to enter Australia at a later date. Tourism activity was assumed to recover to baseline levels immediately after the lifting of a travel ban. We assumed that after lifting the ban, all the students that could not get in during ban will enter in addition to the new ones, however tourists that did not enter Australia for the ban are not assumed to enter when the ban is lifted. Once the ban is lifted, partially or not, we consider the situation to be normal again, due to not having enough information to base different future assumptions on. It is possible that after lifting of the ban, travel will be reduced from past baseline numbers, which would reduce the risk of importations even more. The daily number of travellers from China to Australia in each month and for each scenario is showed in Table   S2 of the supplementary material.
To then calculate the probable number of those that could be infected we used an epidemiological dataset of confirmed cases of COVID-19 in China collected from WHO situation reports 9 and available in our supplementary materials (Table S1). The dataset includes all confirmed cases in China reported from 31/12/2019 to 23/02/2020. We then assumed that notified cases reflect only 10% of the real new infections per day, due to underreporting, mild cases and asymptomatic infections. This assumption is based on data from Japan 10 , which estimated that only 9.2% of cases in China were notified or detected. This estimate is based on testing of all evacuees from Wuhan to Japan and the documented cases in China at the time 10 . Furthermore it has been showed that a high proportion of infected people will have very mild symptoms 11 which are unlikely to be reported. We then estimated the possible true epidemic curve. In order to project the future incidence cases in China we used a Poisson regression model to fit data from the 5 th (start of the incidence declining) to 23 rd of February and estimated the decreasing rate per day (z) as: Where G(t) is the number of new infected at time t and G 0 is the initial value at time t=0 (Incidence at day 5 of February). Once the decreasing rate z was estimated and the incidence forecasted from 23 of February onwards, we then calculated the number of infected people coming from China every two weeks period, , as:

∑
Where N is the total population of China and is the number of people travelling from China to Australia in every two weeks period. When calculating the prevalence of infection in China, we started from two weeks before the period travelling in order to include the people that could be infected and in a latent state. In scenarios 2 and 3, we assumed a linear declining distribution in time of travel for university students waiting to enter the country after lifting of the travel ban. A full and partial lifting of the ban was examined. In the partial ban, over 150,000 university students can enter Australia, but the just over 80,000 expected tourists not.

Epidemic curve in Australia from cases imported from China
The Studies show a long, mild prodrome of several days before people feel unwell enough to seek medical attention, which is also considered in the model 21 . We conducted a sensitivity analyses on the proportion of asymptomatic people, R0 and the case detection rate in China.
The results are showed in the supplementary material.   (Table 2).

Results
In Figure 3 we show the epidemic curve without and with the ban implemented for 5 weeks followed by a full lifting (scenario 1 and 2) and we show a large impact on averting an epidemic in Australia. In both cases, the model reproduces the 15 notified imported cases reported in Australia between the 20 of January and 8 of February. The modelled epidemic in scenario 2, with the full ban, predicts 57 cases in Australia by the 6 th of March. The notified cases by 6 th of March were 66, however we did not account for imported cases from other countries.
In the epidemic curve for scenario 2, when travel resumes there will be a small surge in cases followed by a decrease and the epidemic can be controlled, with a total of less than 300 cases and about 8 deaths. If the ban was never in place (scenario 1), the epidemic would continue for more than a year resulting in more than 2000 cases and about 400 deaths, in a scenario which considers only localised disease in China.
In each scenario tested, the implementation of the travel ban still reduces the total cases and deaths by about 85%, however in the case of R0 being 3, the travel ban will only delay the epidemic curve pushing the peak about 50 days in time ( Figure 2S). The final number of cases and deaths is most sensitive to the R0 assumption, while it is similarly affected by changing the case detection rate (CDR) in China or the proportion of asymptomatic people.
Indeed increasing the proportion of asymptomatic people by 2.3 times (from 17.9% to 41.6%), the number of cases increase by 4 times (from a total of 124 to 491 cases with ban on or 975 to over 4000 in the scenario of no ban), while increasing the CDR about 66% (from 30% to 50%) results in 31% decrease in number of cases (from 106 to 76 and from 737 to 461 in the case of travel ban on and off respectively), see Figure 3S and Figure 4S. When calculating the number of students and tourists arriving from China, we have assumed that the seasonal excess must largely be attributed to the seasonal movement of international students who we estimate represent the large part of the excess movements at this time, which was the most feasible way to account for the normal business and general tourist movements. However the effect of lunar new year on non-student travel is a limitation on this approach.

Discussion
Our estimate of the true epidemic curve is supported by other studies 10,11,25 , and projected case numbers would change with any change in this estimate. Even if the true number of cases in China is 10 or 100 times that reported, only a fraction of the entire population of China has been infected, which leaves a possibility of a subsequent wave of the epidemic.
Indeed the fraction of remining susceptibles is still too high to stop transmissions, for an R0 equal to 2.2, about 55% of the population is required to be immune to achieve herd immunity The pandemic has since surged globally, with new epicentres in Europe and the United States. We do not consider cases coming in from other countrieshowever, this study illustrates the principle of travel bans and public health impact on epidemic control using China as a case study during a period when the epidemic was largely localised to China. A further limitation is the uncertainty of parameters used, particularly the proportion of asymptomatic cases. Whilst we did not use age weighted assumptions of asymptomatic infection, younger people are more likely to be asymptomatic 20 , which would have the effect of increasing undetected transmissions. We have used a conservative estimate, but if the rate is higher than 40%, the outcomes would be worse.
While it has been showed that distancing measures are highly effective 2,27 a systematic review looking at the effectiveness of travel restrictions 28 , shows that international travel restriction are effective in delaying an epidemic but may not contain it. We also assumed a very optimistic scenario of 80% of contacts being identified, which may not occur with high case numbers, if a high proportion of asymptomatic transmission is occurring, or if selfquarantine is ineffective. In this study we assumed voluntary home quarantine, which is showed to be about 50% effective in R0 reduction 29 , however there could be an increased risk of intra-household transmission infected people to contacts 30