新西伯利亚地区COVID-19传播seir-hcd模型反问题的数据驱动正则化

Pub Date : 2022-03-01 DOI:10.32523/2306-6172-2022-10-1-51-68

O. Krivorotko, N. Zyatkov

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引用次数: 4

摘要

摘要采用7个非线性常微分方程(ODE)系统对新型冠状病毒肺炎(COVID-19)在新西伯利亚地区传播的SEIR-HCD模型的反问题进行了数值研究。反问题是通过对每日COVID-19诊断病例、危重病例和死亡病例的额外测量，确定ODE系统的系数(感染率、感染比例、住院病例、死亡率)和一些初始条件(无症状和有症状感染的初始数量)。由于反问题的病态性，利用COVID-19抗体IgG的附加信息和详细的死亡率统计数据进行正则化。将反问题简化为失配函数的最小化问题。我们采用基于全局(OPTUNA软件)和梯度型方法相结合的数据驱动方法来解决最小化问题。数值结果表明，增加新的信息和详细的统计数据使预测情景增加了2倍。

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DATA-DRIVEN REGULARIZATION OF INVERSE PROBLEM FOR SEIR-HCD MODEL OF COVID-19 PROPAGATION IN NOVOSIBIRSK REGION

Abstract The inverse problem for SEIR-HCD model of COVID-19 propagation in Novosi- birsk region described by system of seven nonlinear ordinary differential equations (ODE) is numerical investigated. The inverse problem consists in identification of coefficients of ODE system (infection rate, portions of infected, hospitalized, mortality cases) and some ini- tial conditions (initial number of asymptomatic and symptomatic infectious) by additional measurements about daily diagnosed, critical and mortality cases of COVID-19. Due to ill-posedness of inverse problem the regularization is applied based on usage of additional information about antibodies IgG to COVID-19 and detailed mortality statistics. The inverse problem is reduced to a minimization problem of misfit function. We apply data-driven ap- proach based on combination of global (OPTUNA software) and gradient-type methods for solving the minimization problem. The numerical results show that adding new information and detailed statistics increased the forecasting scenario in 2 times.

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