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Estimating the distribution of time to extinction of infectious diseases in mean-field approaches
Journal of The Royal Society Interface ( IF 3.9 ) Pub Date : 2020-12-01 , DOI: 10.1098/rsif.2020.0540
Maryam Aliee 1, 2 , Kat S Rock 1, 2 , Matt J Keeling 1, 2
Affiliation  

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).

中文翻译:

估计平均场方法中传染病灭绝的时间分布

许多传染病面临的一个关键挑战是预测特定干预下的灭绝时间。一般来说,这个问题需要使用随机模型,该模型认识到动态的固有的基于个体、机会驱动的性质;然而,随机模型本质上是计算成本高昂的,尤其是当还需要考虑参数不确定性时。确定性模型通常用于预测,因为它们更易于处理;然而,它们无法准确地达到零感染,这使得预测灭绝时间成为问题。在这里,我们借助对感染和恢复过程的有效“生-死”描述来研究确定性模型中的灭绝问题。我们提出了一种估计分布的实用方法,因此具有稳健的均值和预测区间,通过计算它们在生死框架内的不同时刻来计算灭绝时间。我们通过分析简化的易感-感染-易感 (SIS) 动力学以及研究解释非洲昏睡病感染和控制的更复杂和现实的动力学示例,表明这些预测与随机模型的结果非常吻合。布氏冈比亚锥虫)。
更新日期:2020-12-01
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