A model-based tool to predict the propagation of infectious disease via airports.

Epidemics of novel or re-emerging infectious diseases have quickly spread globally via air travel, as highlighted by pandemic H1N1 influenza in 2009 (pH1N1). Federal, state, and local public health responders must be able to plan for and respond to these events at aviation points of entry. The emergence of a novel influenza virus and its spread to the United States were simulated for February 2009 from 55 international metropolitan areas using three basic reproduction numbers (R(0)): 1.53, 1.70, and 1.90. Empirical data from the pH1N1 virus were used to validate our SEIR model. Time to entry to the U.S. during the early stages of a prototypical novel communicable disease was predicted based on the aviation network patterns and the epidemiology of the disease. For example, approximately 96% of origins (R(0) of 1.53) propagated a disease into the U.S. in under 75 days, 90% of these origins propagated a disease in under 50 days. An R(0) of 1.53 reproduced the pH1NI observations. The ability to anticipate the rate and location of disease introduction into the U.S. provides greater opportunity to plan responses based on the scenario as it is unfolding. This simulation tool can aid public health officials to assess risk and leverage resources efficiently.

Sampling for global epidemic models and the topology of an international airport network.

Mathematical models that describe the global spread of infectious diseases such as influenza, severe acute respiratory syndrome (SARS), and tuberculosis (TB) often consider a sample of international airports as a network supporting disease spread. However, there is no consensus on how many cities should be selected or on how to select those cities. Using airport flight data that commercial airlines reported to the Official Airline Guide (OAG) in 2000, we have examined the network characteristics of network samples obtained under different selection rules. In addition, we have examined different size samples based on largest flight volume and largest metropolitan populations. We have shown that although the bias in network characteristics increases with the reduction of the sample size, a relatively small number of areas that includes the largest airports, the largest cities, the most-connected cities, and the most central cities is enough to describe the dynamics of the global spread of influenza. The analysis suggests that a relatively small number of cities (around 200 or 300 out of almost 3000) can capture enough network information to adequately describe the global spread of a disease such as influenza. Weak traffic flows between small airports can contribute to noise and mask other means of spread such as the ground transportation.

Controlling pandemic flu: the value of international air travel restrictions.

BACKGROUND: 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. CONCLUSIONS: International air travel restrictions may provide a small but important delay in the spread of a pandemic, especially if other disease control measures 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 of travel restrictions can be substantial while their costs are minimal, dismissal of travel restrictions as an aid in dealing with a global pandemic seems premature.

A model for the oscillatory motion of single dynein molecules.

Axonemal dynein is the molecular motor responsible for the rhythmic beating of eukaryotic cilia and flagella. An individual axonemal dynein molecule is capable of both unidirectional and oscillatory motion along a microtubule (Nature 393 (1998) 711). We propose a model which links the physical motion of a two-headed dynein molecule to its ATP hydrolysis cycle, and which exhibits both processive and oscillatory behaviors. A mathematical analysis of the model is used to make experimentally testable predictions.