The waiting time for inter-country spread of pandemic influenza

Abstract

Background: The time delay between the start of an influenza pandemic and its subsequent initiation in other countries is highly relevant to preparedness planning. We quantify the distribution of this random time in terms of the separate components of this delay, and assess how the delay may be extended by non-pharmaceutical interventions.

Methods and findings: The model constructed for this time delay accounts for: (i) epidemic growth in the source region, (ii) the delay until an infected individual from the source region seeks to travel to an at-risk country, (iii) the chance that infected travelers are detected by screening at exit and entry borders, (iv) the possibility of in-flight transmission, (v) the chance that an infected arrival might not initiate an epidemic, and (vi) the delay until infection in the at-risk country gathers momentum. Efforts that reduce the disease reproduction number in the source region below two and severe travel restrictions are most effective for delaying a local epidemic, and under favourable circumstances, could add several months to the delay. On the other hand, the model predicts that border screening for symptomatic infection, wearing a protective mask during travel, promoting early presentation of cases arising among arriving passengers and moderate reduction in travel volumes increase the delay only by a matter of days or weeks. Elevated in-flight transmission reduces the delay only minimally.

Conclusions: The delay until an epidemic of pandemic strain influenza is imported into an at-risk country is largely determined by the course of the epidemic in the source region and the number of travelers attempting to enter the at-risk country, and is little affected by non-pharmaceutical interventions targeting these travelers. Short of preventing international travel altogether, eradicating a nascent pandemic in the source region appears to be the only reliable method of preventing country-to-country spread of a pandemic strain of influenza.

Figure 1

The process through which a pandemic is imported. (A) The prevalence in the source region, which determines the probability that a randomly selected traveler is infected at scheduled departure. (B)–(D) Density functions of the time since infection during the early stages of the epidemic in the source region for infected travelers (B) before and (C) after departure screening, and (D) after arrival screening for clinical symptoms. In (B), the step illustrates the probabilistic removal of travelers who have completed their incubation period. In (D), the distribution of time since infection in (C) will have shifted to the right by an amount equal to the flight duration, and cases incubated in-flight may be detected by symptomatic screening, as will those symptomatic cases that were not detected previously. Screening sensitivity for this illustration is 60% on both departure and arrival. (E) Upon entering the community undetected, an infected traveler may initiate a minor (inconsequential) or major epidemic, depending on the characteristics of the disease and public health policy.

Figure 2

Effects of border screening and early presentation. (A) The effects of screening sensitivity andon the probability of escaping detection on both departure and arrival during a 12 hour transit. (B) The effects of screening sensitivity and travel duration on the probability than an infected traveler escapes detection during transit and initiates an epidemic after arrival (assuming no other symptomatic individuals on the same flight are identified). R = 3.5 with no early presentation. (C) The effects of R and the time from symptom onset to presentation on the probability that an infected traveler, having entered the wider community following arrival, will initiate an epidemic. There is no screening.

Figure 3

Components of delay until initiation and effects of border screening. (A) The number of infected people successfully arriving and entering the community of an at-risk country (K_A) on each day following the identification of an outbreak of pandemic type strain influenza, assuming a source region population of 5 million, 400 intending travelers per day, R = 1.5, and three levels of symptomatic screening (solid line = nil, dashed line = 50% sensitivity with individual-based removal, dotted line = 50% sensitivity with flight-based quarantining). (B) Corresponding daily probability of initiation (p_d) as a function of time since pandemic identified. (C) Distribution of the delay time until the initiation (D ₁) of an epidemic in an at-risk country by an infected traveler from a source region.

Figure 4

Components of the delay in at-risk country following initiation. (A) Results of 10,000 simulations (bars) and fitted shifted-Gamma distribution of delay time (D ₂) until 20 concurrent cases occur in the at-risk country, given that an epidemic has been initiated, andequals 1.5 with a serial interval of 2.6 days. (B) The total delay distribution until there are 20 concurrent cases in the at-risk country from when a pandemic type strain of influenza outbreak is identified in a source region with a population of 5 million, 400 intending travelers day⁻¹, an R of 1.5, and three levels of symptomatic screening (solid line = nil, dashed line = 50% sensitivity with individual removal, dotted line = 50% sensitivity with flight-based quarantining).

Figure 5

Effects of interventions on the total delay D. (A) The effects of R on delay-distribution. (B) The effects of daily traveler number on the median delay for different values of R. (C) The effects of the time from symptom incubation until presentation and isolation (t_SP) on the delay-distribution. (D) Additive effects of implementing 100% sensitive border screening (individual removal), the wearing of masks during transit, immediate presentation following symptom onset, and flight-based quarantining on the median delay, assuming 400 travelers per day attempting to depart the source region.