Limits to Forecasting Precision for Outbreaks of Directly Transmitted Diseases

Background: Early warning systems for outbreaks of infectious diseases are an important application of the ecological theory of epidemics. A key variable predicted by early warning systems is the final outbreak size. However, for directly transmitted diseases, the stochastic contact process by which outbreaks develop entails fundamental limits to the precision with which the final size can be predicted. Methods and Findings: I studied how the expected final outbreak size and the coefficient of variation in the final size of outbreaks scale with control effectiveness and the rate of infectious contacts in the simple stochastic epidemic. As examples, I parameterized this model with data on observed ranges for the basic reproductive ratio (R0) of nine directly transmitted diseases. I also present results from a new model, the simple stochastic epidemic with delayed-onset intervention, in which an initially supercritical outbreak (R0 > 1) is brought under control after a delay. Conclusion: The coefficient of variation of final outbreak size in the subcritical case (R0 1) and increased with the delay between the start of the epidemic and intervention, and with the average outbreak size. These results suggest that early warning systems for infectious diseases should not focus exclusively on predicting outbreak size but should consider other characteristics of outbreaks such as the timing of disease emergence. Using a mathematical model, John Drake shows that early warning systems for infectious diseases should not focus exclusively on predicting outbreak size but should consider other characteristics of outbreaks such as the timing of disease emergence. Background: Early warning systems that are used to look for outbreaks of infectious diseases are important in public-health planning. One of the most important things that such early warning systems try to predict is the final size of the outbreak. However, for diseases transmitted directly from person to person (rather than via a mosquito, for example), the precision with which the final size can be predicted is often very low. Why Was This Study Done?: This researcher wanted to study how predictable the final outbreak size of an epidemic is if the effectiveness of control measures and the average number of infectious contacts are known. What Did the Researcher Do and Find?: He developed a mathematical model that took into account the variation in the infectiousness of nine well-studied infectious diseases. He found that for any outbreak that increases slowly, precise forecasts of the final outbreak size will be impossible. This result was especially true for epidemics in which there was a substantial delay in intervention after infection occurred, and the precision of the forecast got worse as the delay between the start of the epidemic and intervention increased, and with the average outbreak size. What Do These Findings Mean?: These results suggest that early warning systems for infectious diseases should not focus just on trying to predict outbreak size because this estimate may be inaccurate, but rather they should instead try to predict other characteristics of outbreaks. These results will be of use to people trying to plan for infectious disease outbreaks, but will not affect how patients are managed individually. Where Can I Get More Information Online?: Based in the United States, the Centers for Disease Control and Prevention (CDC) has a Web site that gives background on how the CDC investigates disease outbreaks, along with details of individual diseases: