As mentioned, a key determinant of the risk of importing the emerged infection is ktπt, the mean number of recently-infected individuals intending to travel into Australia on day t. The source region will, with help from the international community, attempt to keep πt, the prevalence of recently-infected individuals, low. Australia has some ability to control kt, the number of travelers from that region into Australia on day t. For such control one can use methods like that described in Section 3.3 to determine the travel volumes that make the risk of importation acceptable. Such travel restrictions clearly carry considerable economic and political costs.
The effect of restricting travel into Australia from the source region is illustrated in Figure 3.1. When R0 is large (>3), in both Australia and the source region, it is necessary to restrict such travel into Australia to near zero before the delay is increased appreciably. Even for lower values of R0 a worthwhile increase in the delay requires travel to be limited to very low levels. For example, with R0 = 1.5 the median delay until an Australian outbreak gathers momentum is 56 days when 400 travelers arrive from the source region per day. The median is increased by only 9 days when the travel volume is reduced to 100 per day, and by another 16 days when the travel volume is reduced to 10 arrivals per day.
It is important to realise that while stringent travel restrictions into Australia are effective when they are introduced prior to the importation of the infection into Australia, they usually provide very little benefit once the epidemic has gathered momentum in Australia.