TY - JOUR

T1 - Mathematical Modeling of the Wuhan COVID-2019 Epidemic and Inverse Problems

AU - Kabanikhin, S. I.

AU - Krivorotko, O. I.

N1 - Funding Information: This work was supported by the Mathematical Center in Akademgorodok and the Ministry of Science and Higher Education of the Russian Federation, contract no. 075-15-2019-1675. Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/11

Y1 - 2020/11

N2 - 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).

AB - 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).

KW - coronavirus

KW - COVID-2019

KW - epidemiology

KW - gradient methods

KW - identifiability

KW - inverse problems

KW - mathematical models

KW - nature-like algorithms

KW - ODE

KW - optimization

KW - regularization

KW - tensor decomposition

UR - http://www.scopus.com/inward/record.url?scp=85097307454&partnerID=8YFLogxK

U2 - 10.1134/S0965542520110068

DO - 10.1134/S0965542520110068

M3 - Article

AN - SCOPUS:85097307454

VL - 60

SP - 1889

EP - 1899

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 11

ER -