The comparative modeling studies did not model IATR or entry controls in great detail. Full border controls – 99.9% effective in reducing imported infectives – in Ferguson _et al._ (2006) only delay the epidemic peak. As noted previously, if most countries cooperate on air travel restrictions and information on outbreaks is widely and immediately shared, the global circulation of infectives may be lower. In other words, the global prevalence of pandemic influenza need not be ever rising to diminish the effect of border controls. Germann _et al._ make a simpler assumption that while international air travel will be the dominant mode of infection seeding in most countries, achieving ‘impenetrable’ borders will be prohibitively expensive. However, such considerations did not prevent studies from evaluating NPIs or drug policies that affect many persons or require significant resources.

Two recent studies<sup>62,63</sup> model international air travel within a highly connected or nodal set (105‐155) of major global cities using real flight data and demographics, and attempt to simulate the global spread of pandemic influenza. They introduce similar IATR policies in similar model settings, but obtain differing results. Both models use a stochastic SEIR model for the epidemic in each city, with the proportions of people in various states in a city affected by the number of travelers entering and departing each city. The proportion of the air passengers in the various disease states traveling between two connected cities is identical to the proportion of people in the states in the city of origin. Sequential travel bans – considered more realistic than a simultaneous global shutdown of the air network – begin in each city after a threshold of cases is recorded. This threshold is higher for the first city to have a major outbreak. This framework is biased such that epidemics in each city in the modeled network are near inevitable (containment is not an objective), but the peak in each city may be delayed by the sequential flight bans. This effect manifests in the city imposing restrictions, but also in cities connected to it yet to reach their intervention threshold.

Cooper _et al._ (2006)<sup>62</sup> set the threshold at 1,000 symptomatic cases for the originating city, and 100 for each city thereafter. Even when 99.9% of air traffic was suspended, there was no containment (loosely defined as the low probability of an epidemic in at least some cities), and delays in peaks were small and insignificant for the viability of other control policies. This result was robust to assumptions about the originating city in their model, the timing of the first outbreak, the initial susceptibility of populations, and infectiousness (only at very low _R0_ values was there significant delay).

Epstein _et al._ (2007)<sup>63</sup> use a flat threshold of 1,000 cases for their baseline modeling of sequential flight bans. The results obtained are slightly less bleak on the effectiveness of IATR – a 95% reduction in flight volume would produce a delay of two to three weeks at _R0_ =1.7, and hence a reduction in the total global cases after 6 months. At the baseline, there is little or a worsening effect with IATR, depending on the timing of the first outbreak<sup>64</sup> , on total cases over the entire pandemic. The results are sensitive to the originating city (delays are larger with Hong Kong than London). The authors model the use of a vaccination policy in tandem with IATR and find that the mixed strategy greatly boosts the effect on the attack rate. Adding a policy of 0.1% daily vaccination – which can be applied to larger number of people thanks to the delay in epidemic peaks achieved by IATR – would reduce the number of cases in urban areas of the US from 102 million to 57 million. This insight follows discussion previously in the context of the studies by Ferguson _et al._ (2006) and Germann _et al._ The 2‐3 weeks delay in itself would also allow many more cities to get ready with NPIs.

These results are not encouraging for IATR proponents looking for containment of a global pandemic, i.e., major reduction in the overall number of cases. It is uncertain whether 95% reduction in travel volumes could be achieved with sequential restrictions, but this 31