Susceptible-infected-recovered model with stochastic transmission

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Christian Gouriéroux, Yang Lu
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引用次数: 0

Abstract

The susceptible-infected-recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which results in its lack of flexibility and explains its difficulty to replicate the volatile reproduction numbers observed in practice. We extend the standard SIR model to a semiparametric SIR model, by first introducing a functional parameter of transmission, and then making this function stochastic. This leads to a SIR model with stochastic transmission. Our model is particularly tractable. We derive its closed-form solution and use it to compute key indicators, such as the condition (and the threshold) of herd immunity and the timing of the peak. When the population size is finite and the observations are in discrete time, there is also observational uncertainty. We propose a nonlinear state-space framework under which we analyze the relative magnitudes of the observational and intrinsic uncertainties during the evolution of the epidemic. We emphasize the lack of robustness of the notion of herd immunity when the SIR model is time-discretized.

随机传播易感-感染-恢复模型
易感-感染-康复模型是流行病学模型的基础。然而,该规范仅取决于两个参数,这导致其缺乏灵活性,并解释了其难以复制在实践中观察到的不稳定的复制数。我们将标准SIR模型扩展为半参数SIR模型,首先引入传输函数参数,然后使该函数随机化。这就得到了具有随机传输的SIR模型。我们的模型特别容易处理。我们推导了它的封闭解,并用它来计算关键指标,如群体免疫的条件(和阈值)和高峰的时间。当种群规模有限且观测时间离散时,也存在观测不确定性。我们提出了一个非线性状态空间框架,在该框架下,我们分析了在疫情演变过程中观测和内在不确定性的相对大小。我们强调,当SIR模型是时间离散时,群体免疫的概念缺乏鲁棒性。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
62
审稿时长
>12 weeks
期刊介绍: The Canadian Journal of Statistics is the official journal of the Statistical Society of Canada. It has a reputation internationally as an excellent journal. The editorial board is comprised of statistical scientists with applied, computational, methodological, theoretical and probabilistic interests. Their role is to ensure that the journal continues to provide an international forum for the discipline of Statistics. The journal seeks papers making broad points of interest to many readers, whereas papers making important points of more specific interest are better placed in more specialized journals. The levels of innovation and impact are key in the evaluation of submitted manuscripts.
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