Travel restrictions on their own would generally have little effect on delaying or preventing pandemic influenza viruses from spreading to new countries. But some places with a very small number of travellers per year (generally < 10,000) may be able to escape a pandemic if they impose travel volume restrictions. Examples would include some small islands in the Pacific or Carribean, and small islands in archipelagos. This applet computes the probability that an isolated population could escape a major outbreak (escape probability) given a set of assumptions about the natural history of the disease, travel behaviour and border control. The output is presented, both graphically and in a table, in three different output formats (see section on output values below). The model is intended to provide an indication of the effect of travel volume reductions, which include the combination of voluntary reductions in travel expected during a pandemic as well as restrictions that might be imposed as a control measure.
A publication describing the modeling and results for Pacific Island countries has been submitted to a peer-reviewed journal.
Parameter Explanations
Number of Travellers and Travel Restrictions
- Total number of travellers / year
The total number of travellers reaching a remote place per year without travel restrictions. (This parameter input is ignored in the "Result by Total Travellers"-Tab, where the total number of travellers per year is varied between 0 and 100,000 with a stepsize of 1000.) - Duration of travel (dV) [days]
The expected duration of travel to reach the remote place (exponentially distributed sojourn time). The disease of an infected traveller may progress during travelling. Even if none of the severely sick individuals is going to travel, individuals can become severely sick during travel. However, travellers are assumed not to infect each other. - Travel reduction of moderately sick cases [%]
The fraction of moderately sick cases that will not travel because of their sickness. - Travel reduction of severely sick cases [%]
The fraction of severely sick cases that will not travel because of their sickness - General travel reduction [%]
The travel reduction imposed on all travellers to the remote place (regardless of wheter voluntarily or imposed as a control measure). For example, during the SARS epidemic a 79% voluntarily travel reduction was observed for some destinations. (This parameter is ignored in the "Result by Travel Reduction"-tab, where the general travel reduction is varied between 0% and 100% with a stepsize of 1%.) - Isolated fraction of moderately sick cases [%]
The fraction of moderately sick travellers that will be rejected from immediate entry due to border control interventions. In practice this fraction refers to people who are effectively isolated on arrival and who therefore cannot infect others. - Isolated fraction of severely sick cases [%]
The fraction of severely sick travellers that will be rejected from immediate entry due to border control interventions. In practice this fraction refers to people who are effectively isolated on arrival and who therefore cannot infect others.
Pandemic Influenza Properties
- Basic reproduction number (R0)
The average number of secondary cases a typical single infected case will cause in a population with no immunity to the disease in the absence of interventions to control the infection. It is likely that the basic reproduction number for pandemic influenza will be between 1.5 and 3.5. (This parameter is ignored in the "Result by R0"-Tab, where the value of R0 is varied in the range between 1.0 and 3.5 with a stepsize of 0.05.) - Relative contagiousness without symptoms [%]
The contagiousness of influenza is probably highest during the symptomatic period of a case. The prodromal period and cases with an asymptomatic course of the disease are less contagious. It is assumed (in the default settings) that they are about half as contagious as the symptomatic cases. - Symptomatic fraction [%]
The fraction of symptomatic cases among all infected individuals. It is assumed (in the default settings) that 2/3 infected individuals will have a symptomatic course of the disease, and 1/3 will have an asymptomatic course of the disease. - Severe fraction of symptomatic [%]
The fraction of severe cases among all symptomatic cases. Symptomatic cases can have a moderate or a severe course of the disease. Only cases with a severe course of the disease are assumed to require health worker assistance. It is assumed that half of the symptomatic cases have a severe course of the disease. - Latent period [days]
The expected duration of the latent period (exponentially distributed duration). This is the time from infection to infectiousness. For Influenza A, this duration has a range of 0.7 to 2.8 days and a mean of 1.4 days. - Prodromal period [days]
The expected duration of the prodromal period (exponentially distributed duration). This is the beginning of the infectious period with nonspecific symptoms (prodromal fever). For influenza this period is about half a day. - Infectious (Symptomatic) period [days]
The expected duration of the infectious period (exponentially distributed duration). This is the fully infectious period with typical influenza symptoms. For influenza this period is about 3 to 5 days. - Time window [days]
Time interval that fully contains a pandemic.
Output Values
- Escape Probability:
The probability that the remote place will not experience a major outbreak, given the parameter values and interventions. -
Tab "Result by R0"
This chart draws the escape probability for values of R0 between 1.0 and 3.5. (The parameter setting for R0 is ignored.) This output also shows the global attack rate. This is the infection attack rate (including asymptomatic, moderately sick and severely sick cases) for the world population. In this model, the values for the global attack rate are determined entirely by the basic reproduction number (R0). -
Tab "Result by Travel Reduction"
This chart draws the escape probability for values of the general travel reduction between 0 and 100%. (The parameter setting for general travel reduction is ignored.) - Tab "Result by Total Travellers"
This chart draws the escape probability for values of the total number of travelers per year between 0 and 100,000 (stepsizes of 100). (The parameter setting for the total number of travellers is ignored.)
Limitations
This simple model and applet has a number of important limitations in terms of both its conceptual design and capabilities. Possibly its major limitation is that it deliberately looks at just one border control intervention. In reality, isolated populations attempting to exclude or at least delay pandemic influenza could also include passenger screening for influenza (e.g. exit screening prior to their departure to the destination of interest along with entry screening), quarantine in facilities or in homes, antiviral treatment and prophylaxis, and on-going surveillance in the community. The model is deterministic so does not consider the level of uncertainty around the parameter estimates or give an indication of the level of uncertainty around the escape probability that is calculated.
