Elena Gubar

• PhD
• Professor (Associate) at St Petersburg University

We affirm that information about tax audit probability may be encapsulated and analyzed within the formations of taxpayer networks. Hence, our aim is to analyze how information and its dissemination as an element of tax control affects the evolutionary process of paying taxes driven by networks of economic agents. We show the process of disseminati...

Based on the SEIRD model, we consider that when multiple viruses of different virulence coexist, the more virulent virus will reinfect nodes already infected by the less virulent virus, which we call here Superexposed. Based on the state transitions, the corresponding differential equations and cost functions are established, then building the corr...

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...

Evolutionary games are a developing sub-field of game theory. This branch of game theory is used in the study of the adaptation of large, but finite, populations of agents to changes in the environment. It assumes that each agent has no significant influence on the system. Many scientific areas use the theory of evolutionary games. In particular, i...

The paper analyzes the optimal lockdown policy using the SQAIRD model over a network with three population groups (young, adult, and old). We show that different lockdown policies may be justified by different socioeconomic structures (objective cost functions that are either convex or concave). We also show that a lockdown policy is always better...

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...

This paper is dedicated to investigating the transmission and prediction of viruses within human society. In the first phase, we augment the classical Susceptible-Exposed-Infectious-Recovered (SEIR) model by incorporating four novel states: protected status (P), quarantine status (Q), self-home status (H), and death status (D). The numerical soluti...

The question about the closest symmetrical packing of chemical substance species (molecules, ions, polymer chains, nanoparticles, etc.) is a subproblem of predicting the structure of matter, in particular, the structure of a crystal, information about which makes it possible to predict almost all of its properties. The design of mathematical models...

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...

This preface introduces the special issue on Dynamic Games for Modeling and Control of Epidemics. It showcases 12 papers with timely contributions to dynamic games and their applications to the modeling, analysis, and control of epidemics. The papers in this collection connect dynamic games and epidemic models to address the recent challenges relat...

This thesis is devoted to the spread of virus in human society. First, we modified the original basic epidemiological model, and divide the system into M different types. The optimal control problem is formulated for the changes of compartments in different states. The total cost is then minimized, the Pontryagin maximum principle is used to solve...

In this research paper we modify a classical SIR model to better adapt to the dynamics of COVID-19, that is we propose the heterogeneous SQAIRD model where COVID-19 spreads over a population of economic agents, namely: the elderly, adults and young people. We then compute and simulate an optimal control problem faced by a Government, where its obje...

The current study represents a survey on several modifications of compartment epidemic models with continuous and impulse control policies. The main contribution of the survey is the modification of the classical Susceptible Infected Recovered (SIR) model with the assumption that two types of viruses are circulating in the population at the same ti...

Nowadays many economic fields are dependent on information flows. Information serves as a strategic tool in economics, business and many social processes. In particular, spreading information among taxpayers can be used as a control parameter in tax control. The probability of auditing which encourages tax payments used to be considered as a unique...

The income tax system is the main instrument of fiscal policy that aims to improve income distribution and economic growth, but the problem arises when there is corrupt behavior in that system. While the tax audit is a tax control tool that is costly, the tax system should guarantee, however, the instruments for tax collection. In this research wor...

Encashment process in the ATM network is an essential part of the banks’ activities. Timely encashment process plays an important role in building a good reputation of the bank that helps attract new clients. Uninterrupted work of money collector teams and stable functioning of ATM network requires solving the following major problems: one of them...

Nowadays, epidemic models provide an appropriate tool for describing the propagation of biological viruses in human or animal populations, or rumours and other kinds of information in social networks and malware in both computer and ad hoc networks. Commonly, there are exist multiple types of malware infecting a network of computing devices, or dif...

We developed an extension of the heterogeneous SIR model taking into account that covid-19 was spread over a multilayer network population. Our optimal control model represents viral contagion for three groups of economic agents, namely: the elderly, adults, and young. For deterring such viral contagion, there is no vaccine, but there are treatment...

Nowadays, epidemic models provide an appropriate tool to describe the propagation of biological viruses in human or animal populations, rumors and misinformation in social networks, and malware in both computer and ad hoc networks. It is common that there are multiple types of malware infecting a network of computing devices, and different messages...

Information is a strategic tool in many areas of the economics, business and social processes. Particularly, information can be considered as a control action in the problem of tax control. Following recent studies, we consider the auditing probabilities, which guarantee the absence of tax deviations, as the optimal strategies of the tax authority,...

We build an evolutionary network game of economic agents that choose actions of being either a high-profile or a low-profile economic agent. Those economic agents reside in the vertices of an undirected graph or network given by their types, and their strategic interaction is driven by imitative behavior. Then, the share of types of economic agents...

We study taxpayers' decisions according to their personal income, individual preferences with respect to the audit and tax control information perceived in their social environment. We consider that citizens are classified by two social groups, the rich and the poor. When public authorities are corrupt, we show that the poor group is the most affec...

Recent wide spreading of Ransomware has created new challenges for cybersecurity over large-scale networks. The densely connected networks can exacerbate the spreading and makes the containment and control of the malware more challenging. In this work, we propose an impulse optimal control framework for epidemics over networks. The hybrid nature of...

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...

Recent wide spreading of Ransomware has created new challenges for cybersecurity over large-scale networks. The densely connected networks can exacerbate the spreading and makes the containment and control of the malware more challenging. In this work, we propose an impulse optimal control framework for epidemics over networks. The hybrid nature of...

Nowadays information is an important part of social life and economic environment. One of the principal elements of economics is the system of taxation and therefore tax audit. However total audit is expensive, hence fiscal system should choose new instruments to force the tax collections. In current study we consider an impact of information sprea...

The emergence of new diseases, such as HIV/AIDS, SARS, and Ebola, represent serious problems for the public health and medical science research to address. Despite the rapid development of vaccines and drugs, one challenge in disease control is the fact that one pathogen sometimes generates many strains with different spreading features. Hence it i...

As the number of devices connected to the Internet is growing, the epidemics of malware spreading imposes a serious cyber security problem. It is common that there exist multiple types of malware infecting a network of devices. Periodically scheduled patching is a common way to protect the devices and thwart the malware spreading over a large popul...

Malware is a malicious software which aims to disrupt computer operations, gather sensitive information, and gain access to private computer systems. It can induce various sorts of damage, including economic costs, the leakage of private information, and instability of physical systems, etc. The distribution of antivirus patches in a network enable...

An effective tax system is an important part of economic and social interactions in human society. The key element of the tax system is tax control which provides the main functions of taxation and allows for increasing tax revenue and fees to the state budget. However, total tax audits of a population of taxpayers is economically unreasonable, and...

Many computer viruses cause repeated epidemics of malwares and induce a serious challenge for IT security. IT security needs to apply the countermeasures iteratively during series of epidemic events to stop the propagation process. We consider a modification of Susceptible-Infected-Recovered model with impulses of control and present the model of p...

Tax control is one of the most important tools for the administration of the tax system (fiscal, social, regulatory and control). Tax audit enables to increase the revenue of taxes and fees in the state budget. Assume that each taxpayer can declare his income less then his true income level, however total tax audits of the taxpayers' population is...

The security risks incurred by the spread of malware in computer and wireless networks can be reduced by the immunization of nodes, using security and antivirus patches. Malware, which captures personal and corporate confidential data, induces different damages, including costs generated by the necessity to compensate disclosure of private informat...

The problem of forming herd immunity to an infectious disease, i.e. influenza, which is optimal to the population, is often considered as a modification of the classical Susceptible-Infected-Recovery model. However the annual vaccination of the total population is quite expensive and is not obligatory for every individual. Any agent in population has...

Tax audit is repeated process which occurs annually. Therefore, we consider a dynamic model of tax auditing in this work. It is supposed that each taxpayer can declare his income less or equal to his true level of income after every tax period. To simplify the model it is also supposed that taxpayers have only two levels of income - low and high. T...

The paper gives a comprehensive presentation of the broad and still developing area of risk-averse decision making in the stochastic linear-quadratic class of multiperson noncooperative differential games and/or distributed controls. The fundamental set of design principles is developed for self-directed decision makers, who are imitatively cautiou...

Strains of influenza viruses spread in human populations during every season of epidemics. As the infected population size increases, the virus can mutate itself and grow in its strength. The traditional epidemic Susceptible-Infectious-Recovered model does not capture the mutations of viruses, and hence the model is not sufficient to study epidemic...

We join on classical SIR model to describe influenza epidemic in urban population with a procedure of making decision. We suppose that agent in urban population makes a choice: whether or not to participate in vaccination company. Each decision involve different costs and indirectly influence on the population state. We formulated an optimal contro...

The main purpose of this work is to optimize cash flow in case of the encashment process in the ATM network with prediction of ATM refusal. The solution of these problems is based on some modified algorithms for the Vehicle Routing Problem and use statistical methods to compile the requests from the ATM network. A numerical example is considered.

The main purpose of this work is research of the agents behavior on the stock market using methods of evolutionary game theory and construct evolutionary dynamics for the long-run period. For this model we consider and compare some additional cases of the dynamics. Following dynamics for the model are constructed: the evolutionary dynamics, the OLG...