The final size and severity of a generalised stochastic multitype epidemic model

Ball, Frank; Clancy, Damian

doi:10.1017/s0001867800025714

Cited by 60 publications

(81 citation statements)

References 15 publications

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“…Properties of the final size distribution for other classes of epidemics can be found in [11][12][13][14]17,20]. The solution given by equations 1 and 2 is for an outbreak in which either (1) epidemiological parameters are naturally such that always R 0 , 1, or (2) public health policy is applied consistently so that intervention is constant and under policy conditions R 0 , 1.…”

Section: Methods Modelmentioning

confidence: 99%

Limits to Forecasting Precision for Outbreaks of Directly Transmitted Diseases

Drake

2005

PLoS Med

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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.

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Section: Methods Modelmentioning

confidence: 99%

Limits to Forecasting Precision for Outbreaks of Directly Transmitted Diseases

Drake

2005

PLoS Med

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“…based on a single observation of cumulative incidence) (Becker, 1989). For theoretical purposes, not only the analysis of single samples of the final size, but also final size distributions of major epidemics have been well analyzed through the so-called Sellke-construction (Andersson and Britton, 2000;Ball and O'Neill, 1999;Ball and Clancy, 1993;Nishiura et al, 2011a). While major epidemics have attracted modelers' interest, little attention has been paid to the final size distribution of minor outbreaks.…”

Section: Introductionmentioning

confidence: 99%

Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks

Nishiura

Yan

Sleeman

et al. 2012

Journal of Theoretical Biology

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Use of the final size distribution of minor outbreaks for the estimation of the reproduction numbers of supercritical epidemic processes has yet to be considered. We used a branching process model to derive the final size distribution of minor outbreaks, assuming a reproduction number above unity, and applying the method to final size data for pneumonic plague. Pneumonic plague is a rare disease with only one documented major epidemic in a spatially limited setting. Because the final size distribution of a minor outbreak needs to be normalized by the probability of extinction, we assume that the dispersion parameter (k) of the negative-binomial offspring distribution is known, and examine the sensitivity of the reproduction number to variation in dispersion. Assuming a geometric offspring distribution with k = 1, the reproduction number was estimated at 1.16 (95% confidence interval: 0.97–1.38). When less dispersed with k = 2, the maximum likelihood estimate of the reproduction number was 1.14. These estimates agreed with those published from transmission network analysis, indicating that the human-to-human transmission potential of the pneumonic plague is not very high. Given only minor outbreaks, transmission potential is not sufficiently assessed by directly counting the number of offspring. Since the absence of a major epidemic does not guarantee a subcritical process, the proposed method allows us to conservatively regard epidemic data from minor outbreaks as supercritical, and yield estimates of threshold values above unity.

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“…This scaling law implies that the average outbreak size ͗n͘ scales as N 1/3 . Moreover, the maximal and the average duration of an outbreak grow as t ‫ء‬ ϳ N 1/3 and ͗t͘ϳln N, respectively.Infection processes typically involve a threshold [1][2][3][4][5][6][7][8][9]. Below the epidemic threshold, outbreaks quickly die out, while above the threshold, outbreaks may take off.…”

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confidence: 99%

Size of outbreaks near the epidemic threshold

Ben‐Naim

Krapivsky

2004

Phys. Rev. E

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The spread of infectious diseases near the epidemic threshold is investigated. Scaling laws for the size and the duration of outbreaks originating from a single infected individual in a large susceptible population are obtained. The maximal size of an outbreak n(*) scales as N(2/3) with N the population size. This scaling law implies that the average outbreak size [n]scales as N(1/3). Moreover, the maximal and the average duration of an outbreak grow as t(*) approximately N(1/3) and [t] approximately ln N, respectively.

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The final size and severity of a generalised stochastic multitype epidemic model

Cited by 60 publications

References 15 publications

Limits to Forecasting Precision for Outbreaks of Directly Transmitted Diseases

Limits to Forecasting Precision for Outbreaks of Directly Transmitted Diseases

Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks

Size of outbreaks near the epidemic threshold

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