The present study examined the effectiveness of selective travel restriction on a heterogeneously mixing population, focusing on full travel restriction among children. The analysis was motivated by two realistic public health issues: (i) children acted as the host maintaining transmission of influenza H1N1-2009 pandemic while adults were relatively less important in transmission [29
] and (ii) the restriction of all international travel is economically damaging, but restricting child travel (e.g. by cancelling school trips) may be more politically feasible and less damaging to the global and local economies. As was expected, preferentially restricting child travels would be more effective than ignoring age or restricting adults. However, our analysis suggests that such a policy would have marginal public health benefits, only slightly reducing the risk of the outbreak in the short term or delaying the outbreak by a few weeks at best. With all but low transmission potential and low degrees of assortativity, selective travel restrictions offer neither a real reduction in the probability of epidemic nor a substantial delay until it takes off.
The effectiveness of selective travel restrictions has not heretofore attracted scientific attention prior to the H1N1-2009 pandemic, although frequent flyers and their role in facilitating international spread have been closely examined [6
]. Many published studies mainly focused on detailed spatial dynamics of transmission in relation to travel restrictions, finding for instance that more than 99% of infected travelers have to refrain from traveling to yield substantial preventive effects [7
]. Given the role of children in propagating H1N1-2009 [13
] (summarized in Table ) and considering the potential to put child-only restrictions into practice, we considered age as an important component to determine the effectiveness of travel restrictions and focused on capturing the role of age-dependency on the mechanism of invasion. Our results indicated that while the effectiveness would be marginally sensitive to assortativity, it would not be substantially effective even with high assortivity.
We make several assumptions in this paper and highlight the most important ones. First, we capture the heterogeneities of transmission networks by stratifying over age but not space. As a result, our findings are conservative in the sense that the actual effectiveness of age-structured restrictions may well be slightly greater than those presented here. However, as long as adults can also contribute to generating local child secondary cases, it is natural that adult travel will eventually lead to an epidemic and substantial involvement of adults in transmission would not delay the outbreak substantially.
Second, since our study rests on a simple statistical model, it has a number of further limitations. We describe the generation time distribution via a one-parameter family and it is possible that allowing a second parameter, in making the distribution more realistic, may potentially elevate the probability of extinction [23
]. Furthermore, it should be remembered that the success of travel restriction depends on travel volume, and this can substantially vary across the world. We examined a plausible number of 10 imported cases per day for the first 50 days through a single port of entry, the scenario most likely to allow effective border closures, but countries with much fewer importations can potentially expect some naturally-occurring delay (e.g. small island nations in Melanesia). Moreover, big countries with multiple ports of entry (e.g. USA and Australia), countries with unmonitored land borders (e.g. those within the Schengen area) and shorter distance of school trip among school-age children as compared to intercontinental travel by adults could prevent the implementation of such a strategy even if it were effective in territories such as Hong Kong. To improve our understanding of this subject further, it might be valuable to account for more detailed heterogeneity (e.g. household and community) and other outcome measurements (e.g. timing and height of epidemic peak), as well as the additional effect of entry screening policies on top of travel restrictions [34
], which would help further our understanding of the effectiveness of travel restrictions in realistic settings. Moreover, we should be able to estimate and compare the cost of available policy options. To help relevant policy decisions in the future, we would need more objective epidemiological criteria concerning the severity of disease or an imminent public health risk by elaborating epidemiological details of descriptions given in International Health Regulations [12
]. The decision may also depend on other available options of control (e.g. if it were realistic to contain an outbreak at local levels, we would not need travel restrictions).
Despite the presence of various realistic features to be explored, the present study has demonstrated that a key policy question can be answered at least qualitatively using a simple statistical model. In conclusion, selective travel restriction of child travelers would have minimal impact on the risk and timeline of an outbreak, even in scenarios most favorable to this strategy. Our findings add to the growing body of evidence that travel restrictions are not viable public health solutions in the face of an emergent influenza pandemic.