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Mathematical Modeling of the Wuhan COVID-2019 Epidemic and Inverse Problems
Computational Mathematics and Mathematical Physics ( IF 0.7 ) Pub Date : 2020-12-08 , DOI: 10.1134/s0965542520110068
S. I. Kabanikhin , O. I. Krivorotko

Abstract

Mathematical models for transmission dynamics of the novel COVID-2019 coronavirus, an outbreak of which began in December, 2019, in Wuhan are considered. To control the epidemiological situation, it is necessary to develop corresponding mathematical models. Mathematical models of COVID-2019 spread described by systems of nonlinear ordinary differential equations (ODEs) are overviewed. Some of the coefficients and initial data for the ODE systems are unknown or their averaged values are specified. The problem of identifying model parameters is reduced to the minimization of a quadratic objective functional. Since the ODEs are nonlinear, the solution of the inverse epidemiology problems can be nonunique, so approaches for analyzing the identifiability of inverse problems are described. These approaches make it possible to establish which of the unknown parameters (or their combinations) can be uniquely and stably recovered from available additional information. For the minimization problem, methods are presented based on a combination of global techniques (covering methods, nature-like algorithms, multilevel gradient methods) and local techniques (gradient methods and the Nelder–Mead method).



中文翻译:

武汉COVID-2019流行病和逆问题的数学建模

摘要

考虑了新型COVID-2019冠状病毒传播动力学的数学模型,该模型于2019年12月在武汉爆发。为了控制流行病学情况,有必要开发相应的数学模型。概述了由非线性常微分方程(ODE)系统描述的COVID-2019传播的数学模型。ODE系统的某些系数和初始数据未知,或指定了它们的平均值。识别模型参数的问题被减少到最小化二次目标函数。由于ODE是非线性的,因此逆流行病学问题的解可以是唯一的,因此描述了分析逆问题的可识别性的方法。这些方法使得可以确定哪些未知参数(或其组合)可以从可用附加信息中唯一且稳定地恢复。对于最小化问题,基于全局技术(覆盖方法,类自然算法,多级梯度方法)和局部技术(梯度方法和Nelder–Mead方法)的组合提出了方法。

更新日期:2020-12-08
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