Author: John Drake
Position: No occupation was given
Institution: National Center for Ecological Analysis and Synthesis
E-mail: drake@nceas.ucsb.edu
Submitted Date: March 30, 2005
Published Date: March 30, 2005
This comment was originally posted as a “Reader Response” on the publication date indicated above. All Reader Responses are now available as comments.

The development of early warning systems (EWS) for epidemics of infectious diseases based on recurrent statistical patterns in other kinds of information, particularly data on climate, is an active area of research [1, 2]. Judging from the estimated burden of diseases for which EWS might be developed, such systems, if effective, would contribute greatly to human welfare and could potentially save many lives [2]. According to a recent report [2], EWS have two principal aims: (i) to identify whether an epidemic will occur, and (ii) to predict the number of cases that will result. For directly transmitted diseases, this second aim may be unattainable at desired levels of precision, regardless of the quality of information.

As an example, in a recent report on the relationship between climate and outbreaks of meningococcal meningitis, the authors find that the timing of epidemics is highly predictable from information on the dynamics of a seasonal weather pattern, the Harmattan winds, but that the final epidemic size is not [1]. This finding is not surprising. The characteristics of disease outbreaks, particularly outbreaks of emerging diseases to which human populations are highly susceptible, prevent highly precise forecasts.

The reason that precise estimates of the final epidemic size cannot be obtained can be understood intuitively. Consider the following description of a typical outbreak. Characteristically, an outbreak begins with a small number of initially infectious individuals. Subsequent infectious contacts are mediated by a wide range of social interactionscontacts within and among households and communitiesso that even individuals that are virtually identical can differ considerable in the number of secondary infections they cause. This is a micro-scale cause of variation as compared with macro-scale, population-level sources of variation. The important implication for EWS is that in such situations, especially where the basic reproductive ratio (R0) is initially very high but is rapidly reduced (perhaps by public health interventions), small deviations in the realized number of infectious contacts are amplified to result in relatively large variation in the final size of the outbreak. Because this variation reflects differences in individual behavior and not macroscopic characteristics of epidemic spread, it is unlikely that climate or other data contain any information about this source of variation (though such data do contain information about macroscopic variation).

A more formal explanation of this phenomenon can be based on a simple model of an epidemic in which EWS captures all macroscopic causes of variation in the final epidemic size but no microscopic causes. Obviously, EWS cannot realistically be expected to capture even all the macroscopic information. Thus, this limit to precision is a fundamental limit and should be interpreted as a theoretical upper bound on forecast precision. The simplest case considers a disease with only two macroscopic epidemiological characteristics, an infection rate and a removal rate, which might change over time as in the case of meningococcal meningitis. In particular, we assume that there is no immunity in the population and that infection and removal are independent in time. This model of disease dynamics belongs to a class of stochastic processes known as non-homogeneous birth-death processes, which, conveniently, turn out to be reasonably tractable. Indeed, more than fifty years ago, Kendall [3] showed how models for the mean and the variance in the final epidemic size are affected by these parameters. The variance can be interpreted as a measure of the precision with which the final epidemic size can be predicted. Kendalls results can be decomposed to show that this quantity is the sum of the average final epidemic size and another quantity minus one. For most realistic epidemiological parameters this other quantity, which is related to the covariance between final epidemic size and the size of the infected population, will be much greater than one. In these cases, the variance in the final epidemic size will be much greater than the average final epidemic size itself.

This fundamental limit to the precision of forecasts does not imply that EWS cannot be used effectively to plan for responding to outbreaks. Rather, it suggests what expectations of EWS are reasonable. Further, as the precision with which forecasts of the final epidemic size can be obtained will depend on many disease-specific properties and maybe other factors, too, case studies of the potential effectiveness of EWS for different diseases are needed. These studies should exploit recent advances in modeling birth-death processes [4] to gain further understanding of the differences among diseases and the causes of geographic variation in the intensity of epidemics. Finally, notwithstanding limits to precision, the benefits to be obtained from estimates of the average final epidemic size and the timing of epidemics alone may warrant considerable investment in EWS.

1. Sultan B, Labadi K, Gugan J-F, Janicot S (2005) Climate drives the Meningitis epidemics onset in West Africa. PLoS Medicine 2: 43-49. 10.1371/journal.pmed.0020006

2. World Health Organization (2004) Using climate to predict infectious disease outbreaks: a review. WHO/SDE/OEH/04.01.

3. Kendall DG (1948) On the generalized birth-and-death process. Annals of Mathematical Statistics 19: 1-15.

4. Dorman KS, Sinsheimer JS, Lange K (2004) In the garden of branching processes. SIAM Review 46: 202-229.