# Olga I. KrivorotkoInstitute of Computational Mathematics and Mathematical Geophysics SB RAS | ICMMG · Laboratory of Mathematical problems of Geophysics

Olga I. Krivorotko

Doctor of Philosophy

## About

48

Publications

4,709

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207

Citations

Citations since 2017

Introduction

## Publications

Publications (48)

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...

The paper presents classification and analysis of the mathematical models of COVID-19 spread in different groups of populations such as the family, school, office (3-100 people), neighborhood (100-5000 people), city, region (0.5-15 million people), country, continent and the world. The classification covers the main types of models including time-s...

A sensitivity-based identifiability analysis of mathematical model for partial differential equations is carried out using an orthogonal method and an eigenvalue method. These methods are used to study the properties of the sensitivity matrix and the effects of changes in the model coefficients on the simulation results. Practical identifiability i...

The information propagation in online social networks is characterized by a nonlinear partial differential equation with the Neumann boundary conditions and initial condition (source) that depends on the type of information and social network. The problem of source identification using additional measurements of the number of influenced users with...

The paper presents the results of sensitivity-based identif iability analysis of the COVID-19 pandemic spread models in the Novosibirsk region using the systems of differential equations and mass balance law. The algorithm is built on the sensitivity matrix analysis using the methods of differential and linear algebra. It allows one to determine th...

The differential evolution algorithm is applied to solve the optimization problem to reconstruct the production function (inverse problem) for the spatial Solow mathematical model using additional measurements of the gross domestic product for the fixed points. Since the inverse problem is ill-posed the regularized differential evolution is applied...

The problem of identification of coefficients and initial conditions for a boundary value problem for parabolic equations that reduces to a minimization problem of a misfit function is investigated. Firstly, the tensor train decomposition approach is presented as a global convergence algorithm. The idea of the proposed method is to extract the tens...

The monitoring, analysis and prediction of epidemic spread in the region require the construction of mathematical model, big data processing and visualization because the amount of population and the size of the region could be huge. One of the important steps is refinement of mathematical model, i.e. determination of initial data and coefficients...

The paper formulates and solves the problem of identification of unknown parameters of mathematical models of the spread of COVID-19 coronavirus infection, based on SEIR type models, based on additional information about the number of detected cases, mortality, self-isolation coefficient and tests performed for the Moscow city and the Novosibirsk R...

The monitoring, analysis and prediction of epidemic spread in the region require the construction of mathematical model, big data processing and visualization because the amount of population and the size of the region could be huge. One of the important steps is refinement of mathematical model, i.e. determination of initial data and coefficients...

We study the identifiability of some mathematical models of spreading TB and HIV coinfections in a population and the dynamics of HIV-infection at the cellular level. Sensitivity analysis is carried out using the orthogonal method and the eigenvalue method which are based on studying the properties of the sensitivity matrix and show the effect of t...

Objectives:
To find residential areas with high incidence rate of tuberculosis in Moscow using spatio-temporal analysis of incidence data.
Methods:
We analyzed the spatial patterns of residence locations of smear or culture positive patients with pulmonary tuberculosis in Moscow. To identify clusters with high local incidence rates the neighborh...

The optimization algorithms for solving multi-parameter inverse problem for the mathematical model of parabolic equations arising in social networks, epidemiology and economy are investigated. The data fitting is formulated as optimization of least squares misfit function. Firstly, the tensor train decomposition approach is presented as global conv...

The differential evolution algorithm is applied to solve the optimization problem to reconstruct the production function (inverse problem) for the spatial Solow mathematical model using additional measurements of the gross domestic product for the fixed points. Since the inverse problem is ill-posed the regularized differential evolution is applied...

In this paper a problem of specifying HIV-infection parameters and immune response using additional measurements of the concentrations of the T-lymphocytes, the free virus and the immune effectors at fixed times for a mathematical model of HIV dynamics is investigated numerically. The problem of the parameter specifying of the mathematical model (a...

A numerical algorithm is proposed to solve the source reconstruction problem for a system of nonlinear shallow-water equations using the dynamics of water surface perturbation measured at a finite number of spatial points and/or over a part of the surface at a fixed time. The combined inverse problem under study is reduced to the minimization of an...

A new combined numerical algorithm for solving inverse problems of epidemiology is described in this paper. The combined algorithm consists of optimization and iterative methods, and determines the parameters specific to a particular population by using the statistical information for a few previous years. The coefficients of the epidemiology model...

A parameter identification problem (inverse problem) for some mathematical models of HIV dynamics and tuberculosis epidemics with experimental observations is investigated. The inverse problems are reduced to a minimization problem. The optimization problem is solved with the help of stochastic methods: a genetic algorithm and fast simulated anneal...

The analysis of biological data is a key topic in bioinformatics, computational genomics, molecular modeling, and systems biology. The methods covered in this article can reduce the cost of experiments aimed at obtaining biological data. The problem of the identifiability of mathematical models in physiology, pharmacokinetics, and epidemiology is c...

A numerical multistep algorithm for computing tsunami wave front amplitudes is proposed. The first step consists in solving an appropriate eikonal equation. The eikonal equation is solved with Godunov’s approach and a bicharacteristic method. A qualitative comparison of the two methods is done. A change of variables is made with the eikonal equatio...

In this paper we present grid methods which we have developed for solving direct and inverse problems, and their realization with different levels of optimization. We have focused on solving systems of hyperbolic equations using finite difference and finite volume numerical methods on multicore architectures. Several levels of parallelism have been...

Analysis of biological data is a key topic in bioinformatics, computational genomics, molecular modeling and systems biology. The methods covered in this article could reduce the cost of experiments for biological data. The problem of identifiability of mathematical models in physiology, pharmacokinetics and epidemiology is considered. The processe...

An algorithm for computing the amplitude of the leading wavefront generated by an impulse source of oscillations is proposed. According to the algorithm, the fundamental solution is represented in the form of the sum of singular and regular components. As a result, the time required for the amplitude computation is reduced by one order of magnitude...

New numerical algorithm of determining the moving tsunami wave height for linear source at the characteristic surface \(t=\tau (x,y)\) is proposed where \(\tau (x,y)\) is a solution of Cauchy problem for eikonal equation. This algorithm based on and representation of fundamental solution of linear shallow water equations in the singular and regular...

We investigate two different inverse problems of determining the tsunami source using two different additional data, namely underwater measurements and satellite wave-form images, and combination of these two inverse problems. We investigate gradient-type methods for inverse problem solutions and show that combination of two types of data allows on...

Four simple mathematical models of pharmacokinetic, competition between immune and tumor cells, infectious disease and tuberculosis epidemic are considered. An optimization approach for identification those models based on gradient type methods is introduced. Inverse problems are formulated in the form of an operator equation and then reduced to th...

Tsunamis are gravitational, i.e. gravity-controlled waves generated by a given motion of the bottom. There are different natural phenomena, such as submarine slumps, slides, volcanic explosions, earthquakes, etc . that can lead to a tsunami. This paper deals with the case where the tsunami source is an earthquake. The mathematical model studied her...

Numerical algorithms for constructing a fundamental solution to the equations of elasticity theory in velocity-stress formulation for an isotropic elastic half-space whose elastic properties (Lame parameters), and the density depend only on depth are considered. An inverse problem is studied to determine the elastic parameters from data of an areal...

In this paper we present a numerical method for solving the Dirichlet problem for a two-dimensional wave equation. We analyze the ill-posedness of the problem and construct a regularization algorithm. Using the Fourier series expansion with respect to one variable, we reduce the problem to a sequence of Dirichlet problems for one-dimensional wave e...

In this paper, we consider an inverse problem of determining the initial condition of an initial boundary value problem for the wave equation with some additional information about solving a direct initial boundary value problem. The information is obtained from measurements at the boundary of the solution domain. The purpose of our paper is to con...

An algorithm to solve numerically the problem of determining the leading edge amplitude of a wave is constructed. The wave is generated by the initial condition u(x, y, 0) = g(y) · δ(x). By the change of variables z = τ(x, y), α = y, where τ is the solution to the eikonal equation τx2+τy2=c-2(x,y) c(x,y) = √gH(x, y), and H(x,y) is the depth at poin...

A numerical method for solving the Dirichlet problem for the wave equation in the two-dimensional space is proposed. The problem is analyzed for ill-posedness and a regularization algorithm is constructed. The first stage in the regularization process consists in the Fourier series expansion with respect to one of the variables and passing to a fin...

An inverse source problem for the wave equation with additional information measured on some parts of the boundary is considered. The degree of ill-posedness of the inverse problem is investigated. A numerical algorithm based on the SVD of a discrete inverse problem is constructed and tested.

We consider new techniques and methods for earthquake and tsunami
related problems, particularly - inverse problems for the determination
of tsunami source parameters, numerical simulation of long wave
propagation in soil and water and tsunami risk estimations. In addition,
we will touch upon the issue of database management and destruction
scenari...

D GIS Research and Information System developed by the World Agency of Planetary Monitoring and Earthquake Risk Reduction (WAPMERR) in cooperation with Informap software development department and the Institute of computational mathematics and mathematical geophysics SB RAS for the purposes of reducing risk due to natural and man-maid hazards and f...