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Estimating the transmission potential of supercritical processes based on the final size distribution of minor
Hiroshi Nishiura1, Ping Yan, Candace K Sleeman
1School of Public Health, The University of Hong Kong, Level 6, Core F, Cyberport 3, 100 Cyberport Road, Pokfulam, Hong Kong; PRESTO, Japan Science and Technology Agency, Saitama 332-0012, Japan. nishiura@hku.hk
Abstract:
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.
Insights
This study estimates reproduction numbers for supercritical epidemics using minor outbreak data. The method applied to pneumonic plague suggests a low human-to-human transmission potential, even with limited outbreaks.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Modeling
Background:
- Estimating reproduction numbers (R0) is crucial for understanding epidemic dynamics.
- Traditional methods often rely on major outbreaks, overlooking data from minor outbreaks.
- The final size distribution of minor outbreaks has not been fully utilized for R0 estimation.
Purpose of the Study:
- To develop and apply a method for estimating R0 from minor epidemic outbreak data.
- To assess the human-to-human transmission potential of pneumonic plague using this novel approach.
- To investigate the sensitivity of R0 estimates to the dispersion parameter (k) of the offspring distribution.
Main Methods:
- Utilized a branching process model to derive the final size distribution of minor outbreaks.
- Applied the model to final size data from pneumonic plague outbreaks.
- Assumed a known dispersion parameter (k) for the negative-binomial offspring distribution and examined sensitivity.
- Normalized the final size distribution by the probability of extinction.
Main Results:
- Estimated the reproduction number for pneumonic plague at 1.16 (k=1) and 1.14 (k=2).
- Results align with transmission network analysis, indicating low pneumonic plague transmission potential.
- Demonstrated that minor outbreaks can be conservatively treated as supercritical for R0 estimation.
Conclusions:
- The proposed method enables R0 estimation from minor outbreaks, providing valuable insights when major epidemics are absent.
- Pneumonic plague exhibits limited human-to-human transmission.
- Directly counting offspring in minor outbreaks is insufficient for assessing transmission potential.
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