Mathematical Modeling of the Wuhan COVID-2019 Epidemic and Inverse Problems
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ATICAL PHYSICS
Mathematical Modeling of the Wuhan COVID-2019 Epidemic and Inverse Problems S. I. Kabanikhina,b and O. I. Krivorotkoa,b,* a
Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia b Novosibirsk State University, Novosibirsk, 630090 Russia *e-mail: [email protected] Received March 2, 2020; revised March 2, 2020; accepted July 7, 2020
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). Keywords: mathematical models, COVID-2019, coronavirus, epidemiology, inverse problems, optimization, regularization, identifiability, ODE, tensor decomposition, nature-like algorithms, gradient methods DOI: 10.1134/S0965542520110068
1. INTRODUCTION In December, 2019, a pneumonia outbreak was reported in Wuhan, China, during which COVID-2019 virus was identified for the first time by analyzing nucleic acid in a patient with pneumonia. According to data from the Chinese Center for Disease Control and Prevention, the reproduction number is estimated as lying between 2 and 3, which corresponds to the number of new infections from a single infection; so long as it is greater than 1, the epidemic will grow (see Figs. 1, 2). A possible source of COVID-2019 virus is bats, since RNA from COVID-2019 samples was found to coincide up to 96% with virus RNA, which was earlier found in Rhinolophus affinis [1]. Virus replication occurs mainly in the lower respiratory tract, causing cytokine overproduction and an immune response in the organism that reduces the number of Т-lymphocytes in the blood, which are responsible for the protective functions of the organism [2]. As of February 11, 2020, the number of confirmed infected cases was 43143 people, of which 1018 were deaths and 4347 were recovered people [3]. Genetically, COVID-2019 is 80% identical to severe acute respiratory syndrome (SARS), an out
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