Introduction

For contagious diseases, to reduce the spread, it is necessary and desirable to quarantine each individual who might have been exposed for a sufficient time for either infection to occur or until it can be assured that there is not likely to be infection (and hence spread of contagion). According to the Centers for Disease Control and Prevention1:

“When someone has been exposed to a contagious disease and it is not yet known if they have caught it, they may be quarantined or separated from others who have not been exposed to the disease. For example, they may be asked to remain at home to prevent further potential spread of the illness. They also receive special care and observation for any early signs of the illness.”

Parenthetically, if an individual manifests progress into a contagious state, subsequent confinement may occur until the contagiousness ends. The question then arises how long should the quarantine of an individual occur to provide assurance that progress to an infectious state would not result.

Sartwell2 conducted one of the first systematic studies on the incubation time for human pathogens and found that a broad spectrum of agents had incubation time distributions that could be modeled as lognormal (although alternative distributional forms were not tested). Leclerc et al. 3 examined the incubation time distribution of a variety of plant pathogens and observed that they could be fit (depending on the pathogen and the plant age) by either the gamma, lognormal, or Weibull distributions. All of these three are skewed right. Williams looked at the theoretical incubation time distribution for pathogens conforming to a stochastic in vivo birth-death process and found that they could also be characterized by a skewed distribution4,5.

In general none of the often used incubation time distributions have a maximum upper limit. In other words

Therefore there is no quarantine time that will provide absolute assurance of no residual risk from contagion. Nishiura6 pointed out the importance of examining the upper tail of the incubation time distribution when assessing the quarantine period following exposure to smallpox. This was also discussed in the context of the SARS coronavirus outbreak7 . Both of these previous authors noted the importance of the distributional form in assessing the upper tail probability, and the influence that data truncation may have on such estimates.

To make use of this approach, an acceptable residual risk needs to be set. To do this, one needs to balance out the costs and benefits of quarantine and risk reduction. For contagious diseases this will require coupling the risk of premature release from quarantine to a disease transmission model such as Legrand et al. 8. This can schematically be shown as in Figure 1. If the costs for enforcing quarantine up to a given time (post exposure) and if the costs associated with releasing individuals at a given time post exposure (with concomitant probability of eventually becoming contagious) can both be estimated, then the optimal quarantine time should be at the intersection of the curves given that both are plotted using the same y-axis. Clearly for pathogens that have a high degree of transmissibility and/or a high degree of severity, the quarantine time should be greater than for agents with lower transmissibility and/or severity. The purpose of this paper is not to estimate where the balancing point should be.

Fig. 1: Schematic of Tradeoff Analysis Needed to Determine Optimum Quarantine Time

The current operative guidance on quarantine periods for Ebola (Zaire) virus is 21 days, based on WHO assessment that the incubation period is 2–21 days 9. A current review of previous outbreaks cites the same range 10. The precise origin of this assessment is unclear, however it is possibly based on the study of the either the 1976 Zaire outbreak11 or 2000 Uganda outbreak12 both of which reported (without detailed analysis) a maximum observed incubation time of 21 days.

This contribution will outline what is known about the incubation time distribution for Ebola (Zaire), and what the potential upper tail percentiles might be. With additional information as outlined above, a formal decision analytic approach to deducing the optimal quarantine time may be devised. In view of the current concerns for the Ebola outbreak in West Africa, illustrations using this organism will be presented.