Estimates of Outbreak Risk from New Introductions of Ebola with Immediate and Delayed Transmission Control - Volume 21, Number 8—August 2015 - Emerging Infectious Disease journal - CDC
Volume 21, Number 8—August 2015
Estimates of Outbreak Risk from New Introductions of Ebola with Immediate and Delayed Transmission Control
The ongoing Ebola outbreak in West Africa, thought to have begun from a single index case in Guinea in December 2013 (1), has produced thousands of cases in Guinea, Sierra Leone, and Liberia (2). This Ebola outbreak is the largest and most widespread since the Ebola virus was discovered in 1976 (3), and the probability of international spread outside of West Africa is not negligible (4). By late April 2015, the virus had been introduced by 7 infected people traveling during their incubation or symptomatic periods to a country other than Guinea, Sierra Leone, or Liberia. Of these 7 cases, 1 led to an outbreak with 19 transmissions in Nigeria (5,6); 1 led to 2 transmissions in the United States (7,8); 1 led to 7 transmissions in Mali (9,10); and 4 led to no transmissions in Mali (11), Senegal (12), the United States (13), and the United Kingdom (14). Additionally, 20 persons who acquired infection in Africa were transferred to the United States and several European countries for treatment (15), leading to 1 transmission in Spain (16).
Although none of these introductions led to a long chain of transmissions, even a small outbreak in a new country can cause societal disruption and disproportionate costs (17). Furthermore, how likely it is that an introduced case will lead to a substantial number of transmissions is unclear, even in settings with a quick and vigorous public health response to new outbreaks. Gomes et al. (4) performed simulations of Ebola outbreaks in each of 220 countries by first estimating the risk of Ebola being exported from Guinea, Liberia, or Sierra Leone by international travelers and then simulating a stochastic Ebola transmission model conditioned on an importation. The model incorporated Ebola transmission from infected persons in the community and hospital settings and from recently deceased Ebola patients. Assumptions used in the model were that only community transmissions are relevant outside of Africa and that transmissions occur at rates corresponding to containment measures already in place. Gomes et al. provided no explicitly numerical probabilities of large outbreaks per importation, but their simulations apparently produced <100 cases in each country.
In another study, Rainisch et al. (18) calculated the estimated number of beds required to treat Ebola patients in the United States by using estimates of importation frequency and subsequent transmission. These researchers reported a high estimate of 7 beds (95% CI 2–13) required at any 1 time; they also provided no numerical probabilities for their estimates.
In our study, we use a branching process model to estimate the probability distribution of outbreak sizes resulting from the introduction of an Ebola case to a new country where the reproductive number R (i.e., expected number of transmissions per case) would likely be quickly, if not immediately, reduced to <1. In this scenario, theory from subcritical branching processes (19), also known as mortal branching processes (20), guarantees that an outbreak will eventually die out, although perhaps not before a substantial number of transmissions occur. In the modeling literature, outbreaks that die out on their own have been called minor outbreaks (21) or stuttering chains (22). Such branching process models have been used to estimate transmission parameters in the context of emerging (22,23) or reemerging (19–21,24) infectious diseases. However, unlike other studies, we used the outbreak final size distribution equations derived from branching process theory to calculate the risk for a large Ebola outbreak under the assumptions of immediate and delayed transmission control after an importation.
Dr. Toth is an assistant professor in the Division of Epidemiology, Department of Internal Medicine, University of Utah School of Medicine, Salt Lake City, UT, USA. His research interest is applied mathematics, specifically mathematical modeling of infection and transmission of pathogens to support risk assessment and intervention planning for public health.
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Suggested citation for this article: Toth DJA, Gundlapalli AV, Khader K, Pettey WBP, Rubin MA, Adler FR, et al. Estimates of outbreak risk from new introductions of Ebola with immediate and delayed transmission control. Emerg Infect Dis. 2015 Aug [date cited].http://dx.doi.org/10.3201/eid2108.150170