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Estimating the distribution of time to extinction of infectious diseases in mean-field approaches
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Aliee, Maryam, Rock, Kat S. and Keeling, Matthew James (2020) Estimating the distribution of time to extinction of infectious diseases in mean-field approaches. Journal of The Royal Society Interface, 17 (173). 20200540. doi:10.1098/rsif.2020.0540
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Official URL: http://dx.doi.org/10.1098/rsif.2020.0540
Abstract
A key challenge for many infectious diseases is to predict the time to extinction under specific interventions. In general, this question requires the use of stochastic models which recognize the inherent individual-based, chance-driven nature of the dynamics; yet stochastic models are inherently computationally expensive, especially when parameter uncertainty also needs to be incorporated. Deterministic models are often used for prediction as they are more tractable; however, their inability to precisely reach zero infections makes forecasting extinction times problematic. Here, we study the extinction problem in deterministic models with the help of an effective ‘birth–death’ description of infection and recovery processes. We present a practical method to estimate the distribution, and therefore robust means and prediction intervals, of extinction times by calculating their different moments within the birth–death framework. We show that these predictions agree very well with the results of stochastic models by analysing the simplified susceptible–infected–susceptible (SIS) dynamics as well as studying an example of more complex and realistic dynamics accounting for the infection and control of African sleeping sickness (Trypanosoma brucei gambiense).
| Item Type: | Journal Article | |||||||||
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| Subjects: | R Medicine > RC Internal medicine | |||||||||
| Divisions: | Faculty of Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | African trypanosomiasis -- Mathematical models, Stochastic analysis, Biomathematics -- Research | |||||||||
| Journal or Publication Title: | Journal of The Royal Society Interface | |||||||||
| Publisher: | The Royal Society Publishing | |||||||||
| ISSN: | 1742-5689 | |||||||||
| Official Date: | 23 December 2020 | |||||||||
| Dates: |
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| Volume: | 17 | |||||||||
| Number: | 173 | |||||||||
| Article Number: | 20200540 | |||||||||
| DOI: | 10.1098/rsif.2020.0540 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access | |||||||||
| RIOXX Funder/Project Grant: |
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