We give a stochastic equation-based model of global pandemic flu. Under a range of assumptions, we project worldwide and U.S. impacts and study the effect of selected interventions. Here, we focus on the U.S. effects of international travel restrictions. Specifically, for various initial outbreaks, we compute the distribution of the First Passage Time (FPT) to the U.S. and number infected in major metropolitan areas worldwide. For a January 1 release in Hong Kong, and assuming no interventions, for example, the mean of this distribution is approx. 18 + 7 days after the first 100 cases are detected at the source. International travel restriction regimes and vaccination-type intervention are then studied. International travel restriction can increase the mean of the FPT distribution substantially. For instance, with 95 % travel restriction, the increase in FPT to the U.S. is approximately 14 days. When other international containment measures are applied, the delay can be much longer. If in the time afforded, control measures such as vaccination are instituted, the result is a significant reduction in cases worldwide and in the U.S. specifically. However, counterintuitively, if travel restrictions are not combined with direct control measures, they can increase the total severity of the U.S. epidemic. This is because restriction-induced delays in passage to the U.S. can push the U.S. outbreak into high epidemic season. This important interaction between policy and seasonality would not be evident without a global-scale model. Finally, in deciding to adopt a policy, one must compare benefits to costs. The cost to the U.S. economy of international air passenger travel restrictions is minimal: on the order of 0.5% of gross national product. Since the benefit of travel restrictions can be substantial while their costs are minimal, their dismissal as an aid in dealing with a global pandemic seems premature.
Planning for a possible influenza pandemic is an extremely high priority, as social and economic effects of an unmitigated pandemic would be devastating. Mathematical models can be used to explore different scenarios and provide insight into potential costs, benefits, and effectiveness of prevention and control strategies under consideration.
Methods and Findings
A stochastic, equation-based epidemic model is used to study global transmission of pandemic flu, including the effects of travel restrictions and vaccination. Economic costs of intervention are also considered. The distribution of First Passage Times (FPT) to the United States and the numbers of infected persons in metropolitan areas worldwide are studied assuming various times and locations of the initial outbreak. International air travel restrictions alone provide a small delay in FPT to the U.S. When other containment measures are applied at the source in conjunction with travel restrictions, delays could be much longer. If in addition, control measures are instituted worldwide, there is a significant reduction in cases worldwide and specifically in the U.S. However, if travel restrictions are not combined with other measures, local epidemic severity may increase, because restriction-induced delays can push local outbreaks into high epidemic season. The per annum cost to the U.S. economy of international and major domestic air passenger travel restrictions is minimal: on the order of 0.8 % of Gross National Product.