Using Mathematical Models to Assess Responses to an Outbreak of an Emerged Viral Respiratory Disease

4.7 Restricting travel within Australia

Page last updated: April 2006

During the 1918-1919 pandemic border restrictions were established between states. It seems that today border restrictions between major cities would at best delay the geographic spread of the epidemic. However, it is useful to know how long it might be for an importation in one location to establish itself in another location. One reason is that this can assist in planning a co-operative response, another is that some regions of Australia might try to isolate themselves.
Travel restrictions between regions in Australia will delay the geographic spread of the epidemic. To illustrate this we consider the effect of travel restrictions on the time delay before an outbreak initiated in Sydney gathers momentum in Melbourne. The results of simulations using the model depicted schematically in Figure 4.9 are presented in Figure 4.10, for four scenarios: (a) R0 = 1.5, with a flat infectiousness function (b) R0=1.5, with a peaked infectiousness function, (c) R0=2.5, with a flat infectiousness function and (d) R0=2.5 with a peaked infectiousness function. The red dotted lines show the time taken for the epidemic to spread from Sydney to Melbourne in the absence of travel restrictions, which are 46, 31, 22 and 15 days for scenarios (a), (b), (c) and (d) respectively. Data on rates of travel are sourced from surveys of domestic visitor nights spent in Sydney and Melbourne (see Tourism Victoria 2005 and Tourism New South Wales 2005), as well as air-travel volumes between the two cities [Australian Bureau of Transport and Regional Economics 2005], and all individuals are assumed to be equally likely to travel.

Schematic of the model used to simulate the effects of travel restrictions. The epidemic growth in each city is described by an SIR model.

Figure 4.9 Schematic of the model used to simulate the effects of travel restrictions. The epidemic growth in each city is described by an SIR model. Travel between cities has been incorporated, so that an epidemic initiated in City 1 can spread to City 2 and vice-versa. The model also contains stochastic effects, so that chance variation in the early stages of an epidemic is taken into account.

The results show that a median delay of up to 50 days in the spread of the epidemic from Sydney to Melbourne can be achieved with scenario (a), which decreases to 33 days in scenario (b), 21 days in scenario (c) and 13 days in scenario (d). However, these median delays require that 99% of travel between Sydney and Melbourne is prevented, and that these restrictions are initiated when there are 20 currently-infectious people in Sydney. If travel restrictions only stop 90% or 80% of travel, respectively, then the delay is reduced to 25 or 18 days in scenario (a), 16 or 11 days in scenario (b), 11 or 7 days in scenario (c) and 7 or 4 days in scenario (d).

To have an appreciable effect it is necessary to apply travel restrictions quite early in the epidemic. The grey panes in Figure 4.10 show the period of time over which the epidemic in Sydney grows from 20 to 1000 currently-infectious people. All travel restrictions have a minimal effect when implemented at a time when Sydney has 1000 infectious cases.

The above results illustrate the effect of internal border control on the spread of epidemic between major centres within Australia, a situation that is also affected by international travel. Unless international borders are also closed, it is likely that the first case in Melbourne would arrive from overseas rather than from Sydney. It is, however, possible that restrictions on travel to and from smaller towns could be used to delay or even stop the spread of an epidemic to more remote areas.
The median delay between the time when a Sydney outbreak reaches 20 current infectives (and there are no cases in Melbourne) and the time when the infection is transmitted to Melbourne and reaches 20 current infectives there.
Figure 4.10 The median delay between the time when a Sydney outbreak reaches 20 current infectives (and there are no cases in Melbourne) and the time when the infection is transmitted to Melbourne and reaches 20 current infectives there.

(a) R0=1.5 and a flat infectiousness function is used,
(b) R0=1.5 and a peaked infectiousness function is used.
(c) R0=2.5 and a flat infectiousness function is used.
(d) R0=2.5 and a peaked infectiousness function is used.

The time at which the travel restrictions are imposed, measured from the arrival of the initial case in Sydney, is varied along horizontal axis. The curves correspond to different percentages of intending travelers prevented from traveling.
The grey shaded region shows the median time between 20 current infectives in Sydney and 1000 current infectives in Sydney.

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