The model includes 155 major cities around the world, including the cities with the 100 busiest airp

Planning for a possible influenza pandemic is an extremely high priority, cheapest car rental canada as social cheapest car rental canada and economic effects of an unmitigated pandemic would be devastating. Mathematical models can be used to explore cheapest car rental canada different scenarios and provide insight into potential costs, benefits, and effectiveness of prevention and control strategies under consideration.
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 cheapest car rental canada States cheapest car rental canada and the numbers of infected persons cheapest car rental canada in metropolitan areas worldwide are studied assuming various times and locations of the initial outbreak. International air travel restrictions cheapest car rental canada alone provide a small delay in FPT to the U.S. When other containment measures are applied at the source in conjunction with travel cheapest car rental canada 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.
International air travel cheapest car rental canada restrictions may provide a small but important delay in the spread of a pandemic, especially if other disease control measures cheapest car rental canada are implemented during the afforded time. However, if other measures are not instituted, delays may worsen regional epidemics by pushing the outbreak into high epidemic season. This important interaction between policy and seasonality is only evident with a global-scale model. Since the benefit cheapest car rental canada of travel restrictions cheapest car rental canada can be substantial while their costs are minimal, dismissal of travel restrictions as an aid in dealing with a global pandemic seems premature.
Copyright: © 2007 Epstein et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, cheapest car rental canada which permits unrestricted use, distribution, and reproduction cheapest car rental canada in any medium, provided cheapest car rental canada the original author and source are credited.
Planning for a possible influenza pandemic is obviously an extremely high priority for the U.S. government. Less obvious, perhaps, is the fact that, in the well-connected world of the 21 st century, no country is isolated from the potential spread of infection. Therefore, there is a pressing need to study the global spread of flu to understand the impact of the global epidemic on U.S. preparedness.
Rvachev and Longini [1] developed a deterministic, equation-based SEIR model to study the role of global air travel in the 1968–1969 cheapest car rental canada influenza pandemic. Recently, others have extended that model to update population levels [2] , [3] , incorporate more recent air travel patterns [2] , [3] , adjust seasonality parameters [2] , [3] , add stochasticity to the model [4] , and extend it to more cities [4] . In general, these models found that, as compared to 1968, epidemics would spread faster and that the order of cities impacted would change under current air travel patterns. In contrast cheapest car rental canada to Colizza, et al . [5] , Cooper, et al . [4] concluded that international travel restrictions do little to reduce the rate of spread cheapest car rental canada globally. Rather, local interventions aimed at reducing transmission cheapest car rental canada are more likely to reduce the rate of spread. Hollingsworth, cheapest car rental canada et al . [6] , using a simplified cheapest car rental canada global model, reached similar conclusions.
Here, we argue that international air travel restrictions sometimes could be useful to slow the progression of pandemic flu and sometimes could be harmful. While travel cheapest car rental canada restrictions alone do little to directly ameliorate the pandemic, they can buy time to develop and deliver vaccine and institute a range of powerful nonpharmaceutical interventions (e.g., social distancing, public education, staging of medical equipment), all of which could sharply cheapest car rental canada reduce cheapest car rental canada cases. Of course, travel restrictions can directly decrease the influx of new infected persons into an area. More importantly, the restrictions reduce the probability of an infected individual leaving the area in which an outbreak is developing. Consequently, travel restrictions are one among a range of strategies that could be used to address cheapest car rental canada a global pandemic. In a recent paper, Brownstein, et al . [7] have presented supporting evidence, showing that the grounding of airplanes in the United States after September 11, 2001 delayed the dynamics of influenza during the 2001–2002 season by approximately 2 weeks. While air travel restrictions in the United States might have a small impact on domestic disease dynamics cheapest car rental canada due to ground transportation, the global spread, such as a transfer of pandemic flu from Asia or Europe to the United States, could be delayed more significantly by international travel cheapest car rental canada restrictions.
From a public health perspective, cheapest car rental canada it becomes clear that the main purpose cheapest car rental canada of travel restrictions is to delay dissemination of the disease until targeted medical and other interventions can be developed and deployed. Even a couple weeks of additional delay is important for the deployment cheapest car rental canada of national cheapest car rental canada and local containment strategies which might not necessarily be related to vaccination per se .
To estimate this delay, we model the distribution of first passage times (FPT) for infected persons to the United States. We define the start of the epidemic as the day on which the first 100 individuals are exposed in a single city, and we define the FPT as the number of days from the epidemic start until the first infected individual crosses the United States border. Seemingly small increases cheapest car rental canada in FPT can translate into significant delays in peak incidence times and values. In all pandemic plans, local social interaction restrictions are recommended. Once these are implemented, the course of the epidemic will be altered. In this model, both simultaneous, global restrictions and sequential, cheapest car rental canada city by city restrictions were tested. The impact of the travel restrictions on both the mean FPT to the United States and the full course of the epidemic are considered, as well as the costs of the intervention.
The initial version of our model was based on (and calibrated to) the global influenza model of Rvachev and Longini [1] , which was based on an earlier model of Baroyan, Mironov, and Rvachev [8] . We have substantially extended and further developed it by adding seasonality in the disease transmission rate, stochasticity, and several possible disease interventions, such as travel restrictions and vaccination. These interventions can be implemented separately or in combination, and either globally or on a city-by-city basis, to test the effectiveness of different intervention scenarios. In addition, populations are made more detailed by including a nonsusceptible class for those individuals who acquired disease immunity either from exposure during previous epidemics to a similar virus or from vaccination.
cheapest car rental canada The model consists of a set of stochastic difference cheapest car rental canada equations describing the disease dynamics within each city and air travel by individuals from one city to another. Time is measured in discrete units of 1 day. The population of each city is divided into mutually exclusive nonsusceptible (NS), susceptible (S), exposed (E), infectious (I), and recovered (R) classes. We do not estimate deaths, although readers can easily compute them by multiplying our infection cheapest car rental canada levels by any assumed case fatality rate. The exposed period is assumed to coincide with the viral incubation period, and the infectious period is assumed to coincide cheapest car rental canada with the symptomatic period. Infectious persons are assumed not to travel. Within each city, individuals are assumed cheapest car rental canada to be well-mixed. Parameter values are the same for all cities. The parameter values used in the model are given in Table S1 . Model equations are given in Text S1 .
The model includes 155 major cities around the world, including the cities with the 100 busiest airports, the 100 largest cities worldwide, and the 52 cities in the Rvachev-Longini model. The 155 cities modeled include 34 major U.S. cities. cheapest car rental canada The population and transportation data have been updated cheapest car rental canada to include year 2000–2004 values. Population data are taken from the U.S. Census cheapest car rental canada Bureau, the United Nations Department of Economic and Social Affairs, the Instituto Brasileiro de Geografia e Estatística, and several other sources [9] – [15] .
Travel data are taken from OAG statistics on flight schedules provided by L. Amaral [16] . The travel network is made more realistic by allowing asymmetric travel between cities. We have also created a modified travel matrix in which we model travel patterns including more than one leg of travel. The methodology for creating this matrix cheapest car rental canada is described in Text S2 .
Natural history parameters for the H5N1 influenza virus align with those used previously [17] – [20] . In particular, the value of R 0 has been chosen to be 1.7. We have also studied a range of R 0 values cheapest car rental canada but specifically focused on the values of 2.0 and 1.4, which in combination with 1.7, correspond to the world pandemics of 1918, 1957, and 1968. Seasonality was implemented based on the assumptions that cities within the tropics have peak viral transmission year round, while in cities outside the tropics, transmissibility varies cheapest car rental canada sinusoidally, with peak transmission occurring on January 1 in the northern hemisphere and on July 2 in the southern hemisphere. To avoid abrupt pattern changes at the boundaries cheapest car rental canada of the tropics, we modeled a smooth latitudinal variation of the amplitude by implementing a corresponding sine wave. In Figures 1A–D for the world and U.S. metropolitan areas we show the dependence of the unmitigated epidemic shapes and the totals for th