These travelers may increase spread of epidemics that have a long generation time, but have little effect on fast-spreading epidemics.

A small proportion of air travelers make disproportionately more journeys than the rest of travelers. They also tend to interact predominantly with other frequent travelers in hotels and airport lounges. This group has the potential to accelerate global spread of infectious respiratory diseases. Using an epidemiologic model, we simulated exportation of cases from severe acute respiratory syndrome–like and influenza-like epidemics in a population for which a small proportion travel more frequently than the rest. Our simulations show that frequent travelers accelerate international spread of epidemics only if they are infected early in an outbreak and the outbreak does not expand rapidly. If the epidemic growth rate is high, as is likely for pandemic influenza, heterogeneities in travel are frequently overwhelmed by the large number of infected persons in the majority population and the resulting high probability that some of these persons will take an international flight.

In today’s world of increasing air travel for both business and pleasure, a small
proportion of persons make disproportionately more journeys than the rest of the population
(

Recent studies of the role of international air travel on the spread of infectious diseases
have highlighted the role of heterogeneities in the connectedness of different airports (

To investigate the role of frequent travelers in the exportation of asymptomatic cases
during the early stages of an epidemic, we simulated outbreaks of both a SARS-like and an
influenza-like airborne respiratory infection in a population in which a small proportion of
the population make many more trips than the rest of the population. In the early stages of
an epidemic, chance events are important because the number of infected persons is small. We
simulated these early stages by using a stochastic model for which every simulation is
different. We present both the mean behavior of the simulations and the range of possible
outcomes across a large number of simulations. In a stochastic model, introduction of 1
infected person has a finite probability of resulting in the rapid extinction of an
infectious disease. To increase the probability of initiating an outbreak, we introduced 3
asymptomatic persons into the population. We simulated the outbreak in a large extended
metropolitan area with a population of 10^{7} persons.

The structure of the model is illustrated schematically in

Schematic representation of the model structure. Black boxes represent infectious
stages and arrows indicate that persons in these populations are allowed to fly. A)
Severe acute respiratory syndrome. Persons with latent infections are not infectious,
and all infectious persons are symptomatic and prevented from traveling. B) Pandemic
influenza. Persons with latent infections are infectious, and a proportion (1
–

The extent to which the high-frequency and low-frequency fliers mix will determine how quickly a disease will spread from the general population to the frequent fliers and vice versa. We simulated the model for a selection of mixing parameters, ranging from wholly random (Φ = 1) to moderate and high levels of assortativeness (Φ = 0.5, 0.25, respectively). For comparison, we also simulated a homogeneous model in which the entire population travels equally frequently.

The outbreak is modeled by dividing the population into those who are still susceptible to
the disease, those who have contracted the disease and are in the latent stage, those who
are infectious and symptomatic, and those who have recovered from the disease (

In our stochastic model, events (such as infection or a person leaving the source area)
occur by chance. For example, the time after symptom onset at which a person recovers from
infection with SARS is not a fixed quantity; rather, it is a randomly chosen time with a
mean of 10 days. _{0}

Description | Parameter | Value
(reference) | |
---|---|---|---|

SARS | Influenza | ||

Infection | |||

Basic reproductive number | _{0} | 2.5 ( | 1.8 ( |

Latent period, d | _{L} | 4 ( | 1.5 ( |

Infectious period, d | _{I} | 10 ( | 1.1 ( |

Generation time, d | _{g}_{L}_{I} | 14 | 2.6 |

Epidemic doubling time, d | _{d}_{g}_{0} | 6.5 | 2.3 |

International travel | |||

Proportion of population who are high-frequency fliers | 0–0.5 | ||

Mixing between groups: Φ = 1, random mixing; Φ = 0, assortative mixing | Φ | 0–1 | |

Relative probability of flying of high-frequency fliers | 20 | ||

Mean probability of flying per day | 0.005 ( | ||

Probability of flying per day of high-frequency fliers | ε_{H} | 0.084 | |

Probability of flying per day of low-frequency fliers | ε_{L} | 0.042 | |

Probability of a case being exported | |||

Homogeneous flying patterns | _{L} | 0.02 | 0.008 |

High-frequency fliers | _{H}_{L}_{H} | 0.34 | 0.13 |

Low-frequency fliers | _{L}_{L}_{L} | 0.017 | 0.006 |

*SARS, severe acute respiratory syndrome.

In our model, we assume that those who are in the latent stage of the disease are not
infectious for SARS and influenza. This is generally accepted to be a good model for SARS
because isolation of symptomatic persons prevented onward transmission of SARS, which
indicated that the latent period has limited or no infectivity (

The disease course of a possible future influenza pandemic is not known. However, studies
of previous pandemics and seasonal epidemics suggest a possible scenario in which the latent
period of influenza may be infectious and not all infected persons will show symptoms (

Little data are available across a population for the relative frequency of flying. The
mean probability of flying for the whole population can be approximated by the number of
airline passengers divided by the population of a country or city. This calculation gives
estimates of 0.005 for Hong Kong, 0.0005 for Beijing, and 0.0002 for Thailand (

We investigated the effect of the setting where the outbreak is initiated by using 2 scenarios. In the first scenario, the outbreak begins among the general, infrequently flying population. Cases subsequently occur among high-frequency fliers as a result of contact between the 2 subpopulations. The mean time until the first high-frequency flier becomes infected is a function of incidence rate in the main population and level of mixing between the 2 groups. In the second scenario, the outbreak begins among the high-frequency fliers. The disease again spreads to the main population because of contacts between the groups, with the mean time until this occurs being a function of the incidence rate in the main population and the level of mixing between the 2 groups.

The mean cumulative number of cases exported (across 50,000 simulations) is presented for
both SARS-like and influenza-like parameters (

As an epidemic progresses, the cumulative number of cases increases, and therefore the
number of asymptomatic cases exported from a source area increases for all travel patterns
(

Mean number of cases exported from a single simulated source epidemic for severe acute
respiratory syndrome–like parameters (A) and influenza-like parameters (B)
(50,000 runs; parameters are listed in

Mixing pattern | First case | No. cases exported,
mean, median (5th–95th percentile) | ||||
---|---|---|---|---|---|---|

Day 10 | Day 20 | Day 30 | Day 40 | Day 50 | ||

SARS | ||||||

Homogeneous flying patterns | 0, 0 (0–0) | 0, 0 (0–1) | 1, 0 (0–3) | 3, 1 (0–7) | 7, 5 (1–16) | |

Random mixing | High | 1, 0 (0–2) | 2, 0 (0–2) | 2, 1 (0–3) | 4, 2 (1–7) | 7, 5 (2–14) |

Low | 0, 0 (0–0) | 0, 0 (0–1) | 1, 0 (0–3) | 3, 1 (0–6) | 7, 5 (1–15) | |

Moderately assortative | High | 2, 1 (0–3) | 3, 2 (1–4) | 4 (3, 1–7) | 6 (4, 2–12) | 9, 7 (2–20) |

Low | 0, 0 (0–0) | 0, 0 (0–1) | 1, 0 (0–2) | 3, 1 (0–6) | 7, 5 (0–15) | |

Highly assortative | High | 2, 1 (0–3) | 4, 2 (1–7) | 5, 5 (2–13) | 10, 8 (3–22) | 16, 12 (4–38) |

Low | 0, 0 (0–0) | 0, 0 (0–1) | 1, 0 (0–2) | 3, 1 (0–6) | 6, 4 (1–15) | |

Influenza | ||||||

Homogeneous flying patterns | 1, 0 (0–1) | 8, 5 (0–20) | 107, 85 (1–251) | 1,268, 1,069 (7–3,118) | 15,729, 13,541 (73–35,132) | |

Random mixing | High | 1, 0 (0–2) | 7, 5 (0–18) | 89, 74 (1–233) | 1,341, 940 (1–3,049) | 14,592, 11,990 (1–35,632) |

Low | 0, 0 (0–1) | 7, 5 (0–18) | 95, 78 (1– 246) | 1,264, 1,057 (7–3,256) | 15,668, 13,651 (74– 35,231) | |

Moderately assortative | High | 2, 0 (0–3) | 8, 6 (0–32) | 93, 72 (1–231) | 1,288, 1,138 (1–3,387) | 15,505, 14,362 (1–32,134) |

Low | 1, 0 (0–1) | 7, 5 (0–20) | 104, 83 (0–264) | 1,411, 1,213 (0–3,526) | 17,081, 15,850 (0–35,403) | |

Highly assortative | High | 3, 2 (0–7) | 15, 10 (2–41) | 106, 81 (2–291) | 1,166, 840 (2–2,923) | 14,145, 10,770 (2–34,351) |

Low | 0, 0 (0–2) | 12, 0 (0–33) | 164, 139 (0–246) | 1,312, 967
(1–3,231) | 16,592, 12,607
(28–36,643) | |

*Means are shown in |

In an outbreak in which the infection spreads rapidly, such as could potentially occur with
pandemic influenza A (

Later in an epidemic, the mean number of exported cases is similar, regardless of where the
epidemic is seeded or the mixing patterns of the high-frequency fliers and low-frequency
fliers (

Heterogeneities in travel patterns increase the number of exported cases to a greater
extent and for a longer period if the relative frequency of flying of the high-frequency
fliers, _{H}

The probability that an infected person will make an international flight while still
incubating infection and nonsymptomatic is higher for a high-frequency flier than for a
low-frequency flier (

Wherever the epidemic is initially concentrated, the disease will spread to all parts of
the population because of contacts between persons in both groups. The speed with which this
occurs will be a function of the level of mixing between the groups. If high-frequency
fliers mix almost exclusively among themselves, they are unlikely to acquire cases early in
an epidemic in which the first cases emerge in the general population. If, however, they
contract the infection early, this exclusivity serves to speed international spread and this
effect may last well into the epidemic (

When the number of cases becomes large, the expected number of exported cases indicates
that the expected number of exported cases (which may be approximated as the probability of
flying while asymptomatic multiplied by cumulative incidence [

The latent period for influenza is likely to be shorter than that for SARS, which reduces
the probability that any infected person will travel before exhibiting symptoms (

We have simulated an outbreak in a single population by using a relatively simple model.
Similar models have been used for the dynamics of single epidemics in a network of countries
or areas connected by a complex airline network (

Our study and the relatively simple structure of the model were limited by the lack of available data on the travel patterns of persons. Travel patterns may vary with age, sex, occupation, and district or country of origin. To increase our knowledge of these patterns, existing surveys of airline passengers at airports could be extended to ask additional questions on number of journeys per year. However, these surveys would necessarily omit those persons who do not take international flights, who are believed to make up a large proportion of many populations. Any additional information could be valuable for assessing the risk for international spread of diseases from affected areas.

The SARS epidemic in Hong Kong satisfied the criteria we have identified for frequent travelers, which accelerated international spread of an outbreak. The first case-patient with SARS in Hong Kong had contact with other frequent travelers in a hotel and seeded the epidemic in high-frequency travelers. However, SARS has long incubation and infectious periods and only moderate transmissibility. For influenza A, which has much shorter incubation and infectious periods, such heterogeneities have a limited effect on the rate of exportation of cases. Because frequent travelers play a role mainly in the early stages of an epidemic, targeting interventions to these persons is unlikely to be an effective control strategy because such a plan would have to be in place almost immediately.

Finally, estimates of the rate of international spread of respiratory infections that do not consider heterogeneities in behavior may be misleading. If an outbreak begins in a rural area, where persons have a low probability of traveling abroad and mixing with frequent fliers, the time until cases are exported is longer than in outbreaks in which frequent travelers contract infection early in the course of the outbreak. When combined with the vagaries of chance early in the evolution of a new epidemic and the complexities of the international airline network, this variability makes early prediction of the pattern and speed of global spread difficult. This difficulty in predicting whether a particular country is likely to import cases from a currently unknown source area highlights the need for developing a strategy for controlling an outbreak caused by imported cases.

Model Description

Truncated distribution (50,000 runs) of number of cases exported from a single
simulated source epidemic for severe acute respiratory syndrome–like
parameters (A and B) and influenza-like parameters (C and D) (50,000 runs, parameters
are listed in

Mean number of exported cases from 50,000 simulations. Parameters are as in

This study was supported by the European Union , the Wellcome Trust, and the Medical Research Council.

Dr Hollingsworth is a mathematical modeler at Imperial College London. Her research interests include developing models for the design of effective interventions to control epidemic outbreaks of directly transmitted pathogens.