Simulation of COVID-19 Spread Scenarios in the Republic of Kazakhstan Based on Regularization of the Agent-Based Model

We propose an algorithm for modeling scenarios for newly diagnosed cases of COVID-19 in the Republic of Kazakhstan. The algorithm is based on treating incomplete epidemiological data and solving the inverse problem of reconstructing the parameters of the agent-based model (ABM) using the set of available epidemiological data. The main tool for constructing the ABM is the Covasim open library. In the event of a drastic change in the situation (appearance of a new strain, removal or introduction of restrictive measures, etc.), the model parameters are updated taking into account additional information for the previous month (online data assimilation). The inverse problem is solved by stochastic global optimization (of tree-structured Parzen estimators). As an example, we give two scenarios of COVID-19 propagation calculated on December 12, 2021 for the period up to January 20, 2022. The scenario that took into account the New Year holidays (published on December 12, 2021 on http://covid19-modeling.ru ) almost coincided with what happened in reality (the error was 0.2%).

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

The inverse problem for SEIR-HCD model of COVID-19 propagation in Novosibirsk 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 initial 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 approach 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.

Sensitivity and identifiability analysis of COVID-19 pandemic models.

The paper presents the results of sensitivity-based identifiability 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 the parameters that are the least and most sensitive to data changes to build a regularization for solving an identification problem of the most accurate pandemic spread scenarios in the region. The performed analysis has demonstrated that the virus contagiousness is identifiable from the number of daily confirmed, critical and recovery cases. On the other hand, the predicted proportion of the admitted patients who require a ventilator and the mortality rate are determined much less consistently. It has been shown that building a more realistic forecast requires adding additional information about the process such as the number of daily hospital admissions. In our study, the problems of parameter identification using additional information about the number of daily confirmed, critical and mortality cases in the region were reduced to minimizing the corresponding misfit functions. The minimization problem was solved through the differential evolution method that is widely applied for stochastic global optimization. It has been demonstrated that a more general COVID-19 spread compartmental model consisting of seven ordinary differential equations describes the main trend of the spread and is sensitive to the peaks of confirmed cases but does not qualitatively describe small statistical datasets such as the number of daily critical cases or mortality that can lead to errors in forecasting. A more detailed agent-oriented model has been able to capture statistical data with additional noise to build scenarios of COVID-19 spread in the region.

Mathematical modeling and forecasting of COVID-19 in Moscow and Novosibirsk region

We investigate the inverse problems of finding unknown parameters of the SEIR-HCD and SEIR-D mathematical models of the spread of COVID-19 coronavirus infection based on additional information about the number of detected cases, mortality, self-isolation coefficient and tests performed for the city of Moscow and the Novosibirsk region since 23.03.2020. In the SEIR-HCD model, the population is divided into seven, and in SEIR-D - into five groups with similar characteristics and with transition probabilities depending on a specific region. An analysis of the identifiability of the SEIR-HCD mathematical model was made, which revealed the least sensitive unknown parameters as related to additional information. The task of determining parameters is reduced to the minimization of objective functionals, which are solved by stochastic methods (simulated annealing, differential evolution, genetic algorithm). Prognostic scenarios for the disease development in Moscow and in the Novosibirsk region were developed and the applicability of the developed models was analyzed. В работе исследованы задачи уточнения неизвестных параметров математических моделей SEIR-HCD и SEIR-D распространения коронавирусной инфекции COVID-19 по дополнительной информации о количестве выявленных случаев заболеваний, смертности, коэффициенте самоизоляции и проведенных тестах для города Москвы и Новосибирской области с 23.03.2020. В SEIR-HCD модели популяция разделена на семь, а в SEIR-D -- на пять групп со схожими признаками и с вероятностями перехода между группами, зависящими от конкретного региона. Проведен анализ идентифицируемости математической модели SEIR-HCD, который выявил наименее чувствительные к дополнительной информации неизвестные параметры. Задачи уточнения параметров сведены к задачам минимизации целевых функционалов, которые решены с помощью стохастических методов (имитация отжига, дифференциальная эволюция, генетический алгоритм). Разработаны прогностические сценарии развития заболевания в Москве и Новосибирской области и проведен анализ применимости разработанных моделей.

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

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). © 2020, Pleiades Publishing, Ltd.