This is the response of the authors to the above Referee's comments submitted with the revised version of the manuscript.

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Ours is the only study thus far to gauge the broad economic cost of imposing air travel restrictions. We gauge this for the U.S. A comparably detailed economic analysis for every country separately is infeasible. Likewise, estimating the First Passage Time distribution for the U.S., with seasonality, both with and without restrictions, was formidable. We explicitly note that the same analysis could be conducted for every country, and believe our model to be useful in facilitating such further applications. However, this model was funded by the U.S. NIH program MIDAS (Models of Infectious Disease Agent Study), whose main concern was the U.S. Future work can address other countries, of course, and our model will be useful in doing so.

POINT 1

Colizza, et al. (2007) is an excellent paper that was published after we submitted our manuscript. We have cited it in the text and added it to the references. Their treatment differs from ours in a number of ways. We use different Base Case locations and start times. Perhaps for this reason, Colizza’s model (and all others of which we are aware) fails to detect that, when combined with seasonality, international air travel restrictions can make specific country epidemics (notably in the US) larger than without restrictions. We also study the distribution of First Passage Times specifically, which has not been previously emphasized. Finally, there is no serious estimate of costs in Colizza, et al.; merely a verbal claim that restrictions would be economically disruptive. No economist would deny this point, or argue that the costs of restrictions are zero. The issue is whether the benefits outweigh the costs. We, at least, make a serious cost estimate (see below) and find that it is less than 1% of GNP per annum.

POINT 2:

The reviewer raises an important point regarding asymptomatic cases. We have added analysis results on this topic and have revised our paper accordingly. In line with other analyses (Longini, et al., 2005, Germann, et al., 2006, Colizza, et al., 2007), we now report results for 33% of cases being asymptomatic, with asymptomatic infectiveness estimated as 50% of normal infectiveness. Our effective contact rate was adjusted commensurately, to recover the original effective R0 (that is, to preserve our original estimate of R0 = 1.7).

POINT 3:

In Comment # 3, the Reviewer questions our use of 1000 cumulative cases as the threshold for implementation of international travel restrictions. There are two issues: first, the use of a single value rather than different city-specific values, and second, the specific value of 1000 cases. Be assured that we thought hard about both of these issues; our choices were based on parsimony and conservatism.

As a modeling assumption, the choice of a single fixed threshold was based on parsimony. As the reviewer suggests, it seems likely that different countries would have different thresholds. However, lacking detailed data to support city-specific estimates, we chose not to add further model complexity based on undocumented hypotheses. The reviewer suggests normalizing to the population size. In fact, if one wished to make a country-specific estimate, the actual syndromic surveillance capability, not the population size, would be the operative factor. Again, however, lacking sufficient data to make this kind of detailed discrimination among cities, we chose not to attempt it.

The base case value of 1000 infectious cases as the threshold for implementation of travel restrictions was meant as a conservative bound; that is, we chose a relatively high number to ensure that the analysis was not biased in favor of travel restrictions. (Obviously, they look better the earlier they are implemented). That being said, this threshold should not be confused with the onset of local containment measures. Presumably these could begin earlier, and after the first cases are reported anywhere, vigilance will likely increase everywhere. That is, the country response thresholds should fall as the disease spreads. This makes our use of the constant threshold more conservative. So, recognizing that local containment may begin at a lower number of cases, the implementation of international travel restrictions was assumed to begin as late as was plausible, in the interest of analytical conservatism. Even so, the analysis shows them to be of considerable potential benefit and modest cost, a point which no other groups have computed.

POINT 4:

On page 11 of our manuscript we describe the analysis we made of multiple-leg travel. We found that for the particular scenario of primary interest (a January Hong Kong start) the core qualitative findings were insensitive to multiple-leg travel, although some minor quantitative effect was observed. We share the reviewer’s intuition that multiple legs may matter, and agree that this is a fertile topic of future research. But no study can do everything, and a complete sweep of all possible initial release locations and start times was neither practical nor necessary for the purposes of this exposition.

POINT 5.

Good point. We have deleted the misleading phrase: “which is a protection rate comparable to a poorly matched vaccine.” We have also clarified our base case vaccination assumptions.

POINT 6.

The reviewer seems to be raising a complex issue: how seasonality and travel restrictions would combine to affect hospital surge requirements. He/She mentions Figure 4A in this regard. However, surge requirements have to do with peak demand for medical services (i.e., the maximum of the epidemic curve), while overall requirements have to do with the area under the epidemic curve, as it were.
For a Hong Kong start, if the pandemic begins in July, then travel restrictions both delay and depress the peak, giving more time to prepare for the surge, as well as reducing the surge demand. If the epidemic begins in January, peak demand is greater with travel restrictions than without them and is not delayed, although the early peak observed without travel restrictions is suppressed (see the red curve in Figure 4A). It is thus a rather complicated comparative tale that we felt would clutter the main narrative.

POINT 7

Proceeding seriatim (R for Reviewer; A for author):

R: “100% travel restrictions could be not only economically disruptive, but also socially disruptive. “

A: We did not deny that international travel restrictions would be disruptive. Indeed, we offer the only published estimate of their economic cost. And to be sure, that cost is positive (though we believe over-rated by this reviewer, see below). But to an economist, the issue is whether the benefits (measured in delay time in which to prepare, and in cases thereby avoided) exceed the costs. Seen in this light, we might prefer to endure some economic disruption if this would avoid large numbers of deaths. This is what we are suggesting, not that costs per se are zero. The estimate of 1% of U.S. GNP is given below, and is now explained more fully in the paper.

R: “Furthermore, people that would be stranded here from other countries would have to be financially supported by the government. “

A: We respectfully disagree. If they were here on business, their companies could support them. Typically, international air travelers are not impoverished, moreover.

R: “Also, all the people working in the airline industry would have to be on paid leave for a year, which would be very costly for the government. “

A: Again, we respectfully disagree. First, the economic impact of the restrictions we consider depends on whether the economy is operating at full employment. If not (as in the U.S. at present), many airline industry workers (managers, executives, baggage handlers, agents, mechanics, etc.) would find alternative employment (i.e., what economists call factor mobility). As for paid leave, some central governments in Europe offer full support for the unemployed, unlike the largely non-unionized U.S. As a matter of fact, 60 percent of the airline industry is non-unionized and individuals were offered no severance when operations ceased after 9/11, for example. However, even if laid off workers were fully compensated, the entire cost of air travel restrictions would still be less than 1% of the U.S. GNP per annum. This is spelled out in detail below and in the paper. In any case, this is hardly a crippling economic perturbation to the $12 trillion U.S. GNP.

R: “Therefore, I believe that the economic impact of a strategy consisting of 100% travel restrictions would be greater than the one presented in the manuscript.”

A: We have completely revamped the discussion of costs in the paper. The upper bound is that our interventions would cost 1% of the U.S. GNP per annum. The reviewer of course is free to dispute the economic analysis, but here it is, clipped from our paper:

“To economists, a cost is the Gross National Product (GNP) loss of the control measure: the value of all economic activity foregone because of its imposition. A central problem in estimating these costs is that for many activities substitutions are possible. So, if one were to close business air travel, the same economic activity (e.g., trades, contracts) may take place electronically (we exclude from this calculation all shipment of goods by sea or by cargo air), with no loss to total output. Likewise, people who had planned to fly to leisure destinations may decide to drive or take a train, or to substitute a new destination, again with no welfare loss. To estimate the full cost in an orthodox fashion, one could develop the full computable general equilibrium model of the entire economy with specific sectors (notably transportation) explicitly represented. One would run that model to equilibrium with all airlines operative. One then would shut down the airlines and rerun the model to (a presumably different) equilibrium. Then one would compare the equilibria and assess the difference. For our present purposes, this is neither feasible nor necessary. Rather, we will develop a conservative upper bound on the cost of the proposed intervention, and show that it is very modest in GNP terms.
First, of the 155 international cities included in the analysis, 34 are U.S. cities with major airports. These account for the activity of airlines classified in the Bureau of Transportation Statistics as Major carriers. Ranked below them in size are the National, Large Regional, Medium Regional, Small Certified, and Commuter carriers [24]. The Major carriers account for just over 85% of the industry’s activity [24]. However, for our bounding calculation we will assume that when they shut down, the entire system shuts down for passenger travel, implicitly eliminating a variety of alternative means of air travel (e.g., using multiple legs on smaller carriers). This conservative assumption overstates the GNP loss. We do assume that freight and cargo air continue to operate, presumably with anti-viral prophylaxis and continuous screening of pilots and crews. Even were air cargo to cease, there would be shipping and land transportation as substitutes, so GNP loss would again be minor. As for private flights for non-business purposes, people may drive or take rail to leisure destinations, or may change destinations. The true cost of an imposed closure is further complicated by the fact that many people would endogenously stop flying, as occurred during the SARS outbreak in 2003, so the loss beyond this endogenous response is difficult to estimate with precision.
With all of this information as background, we estimate the cost of closing the Major airlines as if that were the equivalent of shutting down the entire system, and we will cost it as a simultaneous shutdown, although as discussed above, we model a sequential shutdown. Under these worst case assumptions, the estimated cost falls between $93 billion and $100 billion per annum, extrapolating from the complete and immediate cessation that occurred after 9/11 [25]. Thus, even under the worst case assumption that this economic activity is simply sacrificed, the cost is still around 1% of the $12 trillion U.S. GNP per year [26].
Labor deserves a separate discussion. First, the impact on labor depends on whether the economy is operating at full employment. If not (as in the U.S. at present), many workers (managers, executives, baggage handlers, agents, mechanics, etc.) would find alternative employment (i.e., there would be some factor mobility). For conservatism’s sake, let us assume no such mobility. Roughly 60% of the airline industry remains non-unionized. These individuals received no severance pay after the layoffs of 9/11 and would likely be treated similarly in a pandemic flu shutdown. Severance packages are unlikely; hence, labor costs will not likely weigh heavily on the calculation of costs. We are not condoning this treatment of workers, merely reporting the likely GNP impact. Indeed, a more generous labor policy is altogether feasible. The Senate Joint Economic Committee estimates that “a government funded severance package that covered 100 percent of wages and benefits would cost roughly $500 million per month.” [25] That is $6 billion per year. If this amount were added to the price tag of our policy, the total would rise from $100 billion to $106 billion, increasing the entire cost from 0.8% of GNP to perhaps 0.9%, still very far from ruinous.
In summary, considering substitution possibilities, and even including labor compensation, it is extremely difficult to drive the cost of air travel restrictions beyond 1% of the U.S. GNP per annum.”

R: “Furthermore, it would be more useful to see the global economic impact of travel restrictions.”

A: There are many interesting questions at many levels: global, regional, and local. One cannot study everything in one article. We chose to focus on the U.S. in this paper. That is of interest to many agencies, industries, and individuals, both in the U.S. and elsewhere. The reviewer may have other interests, but we were careful to circumscribe the topic of this particular analysis.

POINT 8.

Good catch, point taken. We have clarified that these limitations are not addressed, but are offered as good faith statements of the study’s boundaries, and as suggestions for further research. We have deleted the claim that “we have addressed.”