Bayesian particle filter algorithm for learning epidemic dynamics
Bayesian particle filter algorithm for learning epidemic dynamics
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DOI：
10.1088/1361-6420/ac2cdc
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发表时间：
2021-11-01
期刊：
影响因子：
2.1
通讯作者：
Somersalo, E.
中科院分区：
文献类型：
--
作者：
Calvetti, D.;Hoover, A.;Somersalo, E.
在本文中，我们考虑了流行病传播的动态模型，特别是 COVID-19，以及基于对新的日常感染的噪声观察来顺序估计未知状态的时间演变和模型参数的逆问题。 COVID-19 的一个特点是，通过与无症状或寡症状感染者接触而发生继发感染的比例很高。由于这些人中的大多数没有被计入每日新增感染人数，因此只能通过基础模型间接推断该群体的规模。用于将当前状态从一个数据实例传播到下一个数据实例的演化模型是经过适当修改的 SEIR 隔室模型，为建模为泊松分布随机变量的新每日感染计数提供预期值。状态和模型参数的估计基于贝叶斯粒子滤波算法。顺序贝叶斯框架自然地提供了对模型参数、基本繁殖数和群体大小估计的不确定性的量化。特别有趣的是，该算法可以估计无症状人群的规模，这是了解 COVID-19 动态和规划缓解措施的关键组成部分。还提出了用于估计疾病传播速度的经典基本繁殖数的替代版本。通过一组计算示例证明了该算法的可行性，其中包括模拟现实数据和来自选定美国县的实际数据。数值测试表明，该算法再现的无症状与有症状队列大小的比率非常接近疾病控制中心目前建议的值。
In this article, we consider a dynamic model for the spread of epidemics, in particular of COVID-19, and the inverse problem of estimating sequentially the time evolution of the unknown state and the model parameters based on noisy observations of the new daily infections. A characteristic of COVID-19 is the significant proportion of secondary infections though contacts with asymptomatic or oligosymptomatic infectious individuals. Since most of these individuals are not accounted for in the number of new daily infections, the size of this cohort can be inferred only indirectly through the underlying model. The evolution model used to propagate the current state from one data instance to the next is a suitably modified SEIR compartment model, providing the expected value for the new daily infection count that is modeled as a Poisson distributed random variable. The estimation of the state and the model parameters is based on a Bayesian particle filtering algorithm. The sequential Bayesian framework naturally provides a quantification of the uncertainty in the estimates of the model parameters, basic reproduction number, and size of the cohorts. Of particular interest is the fact that the algorithm makes it possible to estimate the size of the asymptomatic cohort, a key component for understanding the COVID-19 dynamics, and for planning mitigation measures. Alternative versions of the classical basic reproduction number for estimating the speed of the propagation of the disease are also proposed. The viability of the algorithm is demonstrated through a set of computed examples with both simulated realistic data and actual real data from selected US counties. The numerical tests show that the algorithm reproduces a ratio of asymptomatic vs symptomatic cohort sizes remarkably close to what is currently suggested by the Center for Disease Control.