air travel restrictions may contribute to delaying the glo- bal spread of a pandemic .
lers; no quarantine; and no use of pre-pandemic vaccine or of a vaccine that had been developed after the emer- gence of the new pandemic strain.
While a World Health Organization Writing Group  recognised that islands have achieved border control suc- cesses with pandemic influenza in the past, a more recent review cited expert opinion against the use of mandatory travel restrictions for pandemic influenza control . However this review appeared to be in the context of large countries and did not consider islands (especially low- income island nations which cannot necessarily afford some other control options). Therefore, to better guide the use of these interventions, we aimed to quantify the potential impact of travel volume reductions to prevent (or at least delay) the entry of pandemic influenza into small Pacific island nations.
Assumptions on travel reductions We assumed that voluntary travel reductions (averaged over the course of the pandemic) might be similar to those experienced during SARS for travel between Hong Kong and the United States at 79% . Much higher levels of travel volume reduction (i.e., 99%) were assumed to relate to restrictions imposed by governments of island nations and to reflect essential diplomatic and emergency travel only (or complete "official" border closure with some leakage attributable to illegal yacht movements and private plane use).
Methods Model of a global pandemic and assumptions We considered that a global influenza pandemic would spread around the world via aircraft travel and have an average reproduction number (R0) in the range of 1.5 to 3.0 (with a mid-range value of 2.25). The pandemic was assumed to be in the form of a single pandemic wave that would end within a year.
Travel data We collected travel volume data for all the PICTs that were: (i) members of the Secretariat of the Pacific Com- munity (SPC); (ii) which had a population of under one million (which excluded Papua New Guinea); and (iii) which had an airport (i.e., which excluded Tokelau and Pitcairn Island). Data were from the SPC website  and from its links to the websites of the Statistics Depart- ments/Ministries of the PICTs (where these existed).
For this pandemic scenario, we developed a probabilistic mathematical model that is described in detail in the Technical Appendix (Additional file 1) along with a numerical example for one island nation. An interactive software application that was based on this model was also developed and is freely available online http:// www.influsim.info/software/escaval.
The key parameter calculated was the "island escape prob- ability" which was the probability that an island nation would avoid an outbreak of pandemic influenza for the full course of the global pandemic. The values of the input parameters used in our model for the global pandemic were based on the published model InfluSim  (with ver- sion 2.1, April 2008, being freely downloadable). In addi- tion, we made the two other assumptions to increase model realism:
) were assumed to be well enough to travel.
were assumed to be well enough to travel.
Such assumptions are likely to be very conservative as they assume no exit screening by pandemic-affected nations. We also assumed that no other pandemic influenza con- trol measures would be utilized in the island nations. That is, no entry screening; no provision of antivirals to travel-
Calculating the escape probability Using these data, we expect that a given number of infected individuals enter the island during the global pandemic. Depending on their course of disease and on the remaining time of contagiousness, the expected number of secondary cases per index case varies, and so does the probability that the index case triggers a major outbreak on the island. We combine all possible events, taking into consideration their individual probabilities, to calculate the probability that an island will either experi- ence a major outbreak or ultimately escape the pandemic. Our calculations assume that travel restrictions are per- formed from the very beginning of a pandemic until the end or until the failure to prevent introduction becomes evident.
Results The results (Table 1) indicate that for the 17 PICTs with travel data, only six would be likely to avoid introduction of pandemic influenza, even if the pandemic strain was of relatively low contagiousness (i.e., for R0 = 1.5) and if very tight travel reductions of 99% were applied throughout the course of the global pandemic (Table 1). For more severe pandemics (R0 = 2.25 or higher), only four to five PICTs would have more than 50% probability of escap- ing. Only one country (Tuvalu) was considered to have a high chance of escaping a relatively "mild" pandemic by relying on voluntary travel volume reductions alone (i.e., a 79% reduction level).
Page 2 of 5