Abstract
BackgroundEarly 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 FindingsI 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 (R 0) 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 (R 0 > 1) is brought under control after a delay.ConclusionThe coefficient of variation of final outbreak size in the subcritical case (R 0 < 1) will be greater than one for any outbreak in which the removal rate is less than approximately 2.41 times the rate of infectious contacts, implying that for many transmissible diseases precise forecasts of the final outbreak size will be unattainable. In the delayed-onset model, the coefficient of variation (CV) was generally large (CV > 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.
Highlights
The epidemiological responsibility to forecast disease outbreaks is an onerous one
Warning systems for outbreaks of infectious diseases are an important application of the ecological theory of epidemics
The coefficient of variation of final outbreak size in the subcritical case (R0, 1) will be greater than one for any outbreak in which the removal rate is less than approximately 2.41 times the rate of infectious contacts, implying that for many transmissible diseases precise forecasts of the final outbreak size will be unattainable
Summary
The epidemiological responsibility to forecast disease outbreaks is an onerous one. Because of the devastating consequences and high costs of disease, predicting outbreaks is a chief goal for public-health planning and emergency preparedness. Quantitative forecasting and development of early warning systems (EWSs) for disease outbreak is a high priority for research and development [1]. Intuition suggests that for directly transmissible diseases, the magnitude of the outbreak will be extremely difficult to predict because of the stochastic process of infectious contacts [2,3]. 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. Warning systems that are used to look for outbreaks of infectious diseases are important in public-health planning. 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
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