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The COVID-19 pandemic, etiologically related to a new coronavirus, has had a catastrophic impact on the demographic situation on a global scale. The aim of this study was to analyze the manifestations of the COVID-19 epidemic process, the dynamics of circulation, and the rate of the spread of new variants of the SARS-CoV-2 virus in the Russian Federation. Retrospective epidemiological analysis of COVID-19 incidence from March 2020 to fall 2023 and molecular genetic monitoring of virus variability using next-generation sequencing technologies and bioinformatics methods were performed. Two phases of the pandemic, differing in the effectiveness of anti-epidemic measures and the evolution of the biological properties of the pathogen, were identified. Regularities of SARS-CoV-2 spread were determined, and risk territories (megacities), risk groups, and factors influencing the development of the epidemic process were identified. It was found that with each subsequent cycle of disease incidence rise, the pathogenicity of SARS-CoV-2 decreased against the background of the increasing infectiousness of SARS-CoV-2. Data on the mutational variability of the new coronavirus were obtained using the Russian platform of viral genomic information aggregation (VGARus) deployed at the Central Research Institute of Epidemiology. Monitoring the circulation of SARS-CoV-2 variants in Russia revealed the dominance of Delta and Omicron variants at different stages of the pandemic. Data from molecular genetic studies are an essential component of epidemiologic surveillance for making management decisions to prevent the further spread of SARS-CoV-2 and allow for prompt adaptation to pandemic control tactics.

This study proposes and theoretically substantiates a unique mathematical model for predicting the spread of infectious diseases using the example of COVID-19. The model is described by a special system of autonomous differential equations, which has scientific novelty for cases of complex dynamics of disease transmission. The adequacy of the model is confirmed by testing on the example of the spread of COVID-19 in one of the largest regions of Ukraine, both in terms of population and area. The practical novelty emerges through its versatile application in real-world contexts, guiding organizational decisions and public health responses. The model’s capacity to facilitate system functioning evaluation and identify significant parameters underlines its potential for proactive management and effective response in the evolving landscape of infectious diseases.

Infectious diseases are one of the most important problems of the modern world, for example, the periodic outbreaks of coronavirus infections caused by COVID-19, influenza, and many other respiratory diseases have significantly affected the economics of many countries. Hence, it is therefore important to minimize the economic damage, which includes both loss of work and treatment costs, quarantine costs, etc. Recent studies have presented many different models describing the dynamics of virus spread, which help to analyze the epidemic outbreaks. In the current work we focus on finding solutions that are robust to noise and take into account the dynamics of future changes in the process. We extend previous results by using a nonlinear model-predictive-control (MPC) controller to find effective controls. MPC is a computational mathematical method used in dynamically controlled systems with observations to find effective controls.

The analysis of global epidemics, such as SARS, MERS, and COVID-19, suggests a hierarchical structure of the epidemic process. The pandemic wave starts locally and accelerates through human-to-human interactions, eventually spreading globally after achieving an efficient and sustained transmission. In this paper, we propose a hierarchical model for the virus spread that divides the spreading process into three levels: a city, a region, and a country. We define the virus spread at each level using a modified susceptible–exposed–infected–recovery–dead (SEIRD) model, which assumes migration between levels. Our proposed controlled hierarchical epidemic model incorporates quarantine and vaccination as complementary optimal control strategies. We analyze the balance between the cost of the active virus spread and the implementation of appropriate quarantine measures. Furthermore, we differentiate the levels of the hierarchy by their contribution to the cost of controlling the epidemic. Finally, we present a series of numerical experiments to support the theoretical results obtained.

COVID-19 has become the largest pandemic in recent history to sweep the world. This study is devoted to developing and investigating three models of the COVID-19 epidemic process based on statistical machine learning and the evaluation of the results of their forecasting. The models developed are based on Random Forest, K-Nearest Neighbors, and Gradient Boosting methods. The models were studied for the adequacy and accuracy of predictive incidence for 3, 7, 10, 14, 21, and 30 days. The study used data on new cases of COVID-19 in Germany, Japan, South Korea, and Ukraine. These countries are selected because they have different dynamics of the COVID-19 epidemic process, and their governments have applied various control measures to contain the pandemic. The simulation results showed sufficient accuracy for practical use in the K-Nearest Neighbors and Gradient Boosting models. Public health agencies can use the models and their predictions to address various pandemic containment challenges. Such challenges are investigated depending on the duration of the constructed forecast.

In the current study, we define a hierarchical epidemic model that helps to describe the propagation of a pathogen in a clustered human population. The estimation of a novel coronavirus spreading worldwide leads to the idea of the hierarchical structure of the epidemic process. Thus, the propagation process is divided into three possible levels: a city, a country, and a worldwide. On each level, the pathogen propagation process is based on the susceptible-exposed-infected-recovered (SEIR) model. We thus formulate a modified transmission model of infected individuals between levels. The control of the pathogen’s spread can be seen as an optimal control problem. A trade-off exists between the cost of active virus propagation and the design of appropriate quarantine measures. Each level of the hierarchy is defined by its network. A series of numerical experiments was conducted to corroborate the obtained results.

Different strains of influenza viruses spread in human populations during every epidemic season. As the size of an infected population increases, the virus can mutate itself and grow in strength. The traditional epidemic SIR model does not capture virus mutations and, hence, the model is not sufficient to study epidemics where the virus mutates at the same time as it spreads. In this work, we establish a novel framework to study the epidemic process with mutations of influenza viruses, which couples the SIR model with replicator dynamics used for describing virus mutations. We formulated an optimal control problem to study the optimal strategies for medical treatment and quarantine decisions. We obtained structural results for the optimal strategies and used numerical examples to corroborate our results.