论文标题
估计COVID-19的疾病模型的有效繁殖数和变量
Estimating the Effective Reproduction Number and Variables of Disease Models for the COVID-19 Epidemic
论文作者
论文摘要
本文讨论了估算非线性模型中疾病扩散及其应用于COVID-19-19的流行病的问题。重新审视了第一个无约束方法，并证明它们对应于线性过滤器的应用，然后对坐标变化后的有效繁殖数的非线性估计。不受约束的方法通常无法将估计变量保持在其物理范围内，并且可能导致不可靠的估计值，这些估计需要积极地平滑原始数据。为了克服这些缺点，提出了一种约束估计方法，该方法将模型变量保持在预先指定的边界内，并且还可以促进估计值的平滑度。受限的估计可以直接应用于原始数据，而无需进行前平面和相关的信息丢失和其他滞后。它也很容易扩展以处理其他信息，例如感染者的数量。由此产生的问题是将线性和凸二次约束的凸二次优化问题施放。还表明，应用于死亡数据时，不受约束和受约束的方法都与死亡率无关。这些方法应用于COVID-19-19的公共死亡数据。
This paper deals with the problem of estimating variables in nonlinear models for the spread of disease and its application to the COVID-19 epidemic. First unconstrained methods are revisited and they are shown to correspond to the application of a linear filter followed by a nonlinear estimate of the effective reproduction number after a change-of-coordinates. Unconstrained methods often fail to keep the estimated variables within their physical range and can lead to unreliable estimates that require aggressively smoothing the raw data. In order to overcome these shortcomings a constrained estimation method is proposed that keeps the model variables within pre-specified boundaries and can also promote smoothness of the estimates. Constrained estimation can be directly applied to raw data without the need of pre-smoothing and the associated loss of information and additional lag. It can also be easily extended to handle additional information, such as the number of infected individuals. The resulting problem is cast as a convex quadratic optimization problem with linear and convex quadratic constraints. It is also shown that both unconstrained and constrained methods when applied to death data are independent of the fatality rate. The methods are applied to public death data from the COVID-19 epidemic.
