Determining the Required Number of Information Channels Based on the Information Dissemination Model Oleksandr Voitko 1, Volodymyr Cherneha 2, Vladislav Solonnikov 3, Olena Poliakova 4, Roman Korolyov 5 1,2,3,4 National Defense University of Ukraine named after Ivan Cherniakhovskyi, Kyiv, Ukraine 5 Simon Kuznets Kharkiv National University of Economics, Kharkiv, Ukraine Abstract The article considers issues related to the study of processes that characterize the dissemination of information materials, as well as analysis of qualitative characteristics of information to assess the potential coverage of target audiences and the degree of perception of this information by the relevant audience. The purpose of the article is to develop an analytical model for determining the required number of tools (information channels) to achieve certain goals in the implementation of the strategic narrative of the state, taking into account the requirements that affect the dissemination of information. The application of the proposed mathematical tools to determine the required number of tools (information channels) in the interests of implementing the strategic narrative of the state on the basis of analytical model of information dissemination, will reasonably form the need and volume of information and psychological impact on target audiences. , and the quality of news channels. This will provide an opportunity to identify the main tasks for the system of strategic communications and to realize the interests of the state in the form of public support for the strategic course of the state to gain full membership of Ukraine in the EU. Keywords 1 Target audience, narrative, dissemination of information, strategic communications 1. Introduction it is necessary to have an effective and efficient system of strategic communications of the state, which uses a single information space, has reliable Ukraine's integration into the Euro-Atlantic channels of communication with the population security space and the acquisition of NATO and an appropriate branched information membership have been identified as the main goal infrastructure. of Ukraine's Military Security Strategy, which was enacted by the Decree of the President of Ukraine in March 2021. To achieve this goal, 2. General Problem Statement Ukraine will take a set of appropriate measures. One such measure is countering in cyberspace and In previous publications, the authors solved the imposing one's will in the information space [1]. problem of scientific substantiation of accession To organize the implementation of such a task, to the EU, NATO on the basis of analysis of III International Scientific And Practical Conference “Information Security And Information Technologies”, September 13–19, 2021, Odesa, Ukraine EMAIL: o.voytko@ukr.net (A. 1); chevn1980@gmail.com (A. 2); vladislavsolonnikov@ukr.net (A. 3); elena9669@gmail.com (A. 4); korolevrv01@ukr.net (A. 5); ORCID: 0000-0002-4610-4476 (A. 1); 0000-0001-6190-3252 (A. 2); 0000-0002-7653-416X (A. 3); 0000-0003-4370-2187 (A. 4); 0000-0002-7948-5914 (A. 5); ©️ 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org) statistical data of public opinion and forecasting audiences are proposed, and a visualization of the scenarios for its development [2, 3]. information dissemination model is developed The obtained forecast data allowed to [5]. determine the peculiarities of the implementation The purpose of the article is the development of the strategic narrative of the state by the system of an analytical model for determining the of strategic communications and to realize the required number of tools (information channels) interests of the state in the form of public support to achieve certain goals in the implementation of for its strategic course to Ukraine's full the strategic narrative of the state, taking into membership in the EU and NATO. The proposed account the requirements that affect the process of approach will allow to develop effective and dissemination of information. efficient materials of information and psychological impact, which will be implemented 2.1.1. Research results by a system of strategic communications when influencing the relevant target audiences. An Today, along with Ukraine, there are several extremely important task will be to study the states and their associations, more powerful than processes that characterize the distribution of Ukraine, which have interests different from the information materials, as well as the analysis of national interests of Ukraine, and Ukraine is not qualitative characteristics of information to assess the potential coverage of target audiences and the able to resist their aggressive actions alone. degree of perception of this information by the Therefore, joining NATO is one of the government's priorities in order to protect national relevant audience. This article is devoted to the interests. statement of a possible variant of the decision of Public opinion gained very drastic changes in the resulted problems. the direction of European and North Atlantic cooperation with the beginning of the armed 2.1. Analysis of recent research and aggression of the Russian Federation. publications Unfortunately, during the war, Ukrainian society did not get the desired result in terms of proper The armed aggression of the Russian support and national security of Ukraine from the Federation against Ukraine is carried out in EU and NATO. Starting in 2017, the number of various directions of the "hybrid war". Aggressive supporters of such integration began to gradually influences are carried out both simultaneously and decrease. consistently, practically on all spheres of life of Public opinion on EU accession has changed the state, thus the received results in one sphere somewhat depending on the political, military and are at once used for strengthening of influence in economic processes that have taken place in other spheres. To date, a large number of domestic Ukraine over the past two decades. To achieve the and foreign scientists are engaged in research on stated goal of the study, it is not enough for us to "hybrid actions". In the works of Landa D.V., assess only the current distribution of public Danyka Y.G., Salnikova O.F., Snitsarenko P.M. opinion on this issue. It is necessary to identify the and many others, covers materials on the forms general trends of its change in the future, to and methods used by the aggressor to achieve its choose those that are directed in the desired imperial goals, and contains a number of direction for us and are characterized by the theoretical provisions, recommendations on greatest reliability. This was achieved using possible ways to counter. Unfortunately, scientific scientific forecasting, namely the method of publications on the mathematical justification of statistical extrapolation. The analysis of the the necessary forces and means, in achieving obtained results shows that in order to ensure specific goals, are not enough. further positive forecast development of public A number of software services are available on opinion of the population of Ukraine on EU the Internet, with which it is possible to simulate accession it is necessary in 2022 and 2023 to the process of information dissemination. The increase the number of supporters of society in authors with the help of one of such services this direction by 2.4 million people, respectively. (Melting Asphalt) visualized a model of (6.3%) in 2022 and 0.7 million people. (2.1%) in information dissemination among the target 2023 [2]. audience [4]. Indicators that influence the The obtained forecast data provided an dissemination of information among target opportunity to determine the peculiarities of the implementation of the strategic narrative of the B – the number of inactive subscribers to state by the system of strategic communications the channel, i.e. those who have not read the news, and to realize the interests of the state in the form but are subscribers; of public support for its strategic course to C – the number of non-subscribers who Ukraine's full membership in the EU and NATO. did not read the news; An extremely important task will be to study the λ – the intensity of subscribing to a news processes that characterize the distribution of agent; information materials, as well as the analysis of μ – the intensity of unsubscribing from the qualitative characteristics of information to assess news agent; the potential coverage of target audiences and the ξ – intensity of reading the news. degree of perception of this information by the With the initial conditions at the time 𝑡 = 0: relevant audience. In order to calculate the 𝐴(0) = 𝐴0 , 𝐵(0) = 𝐵0 , 𝐶 (0) = 𝐶0 . required number of information channels that will 𝐴0 > 0, 𝐵0 > 0, 𝐶0 > 0. be used in the implementation of the strategic The solution of this system of equations can be narrative of the state, it is necessary to calculate presented as follows: the corresponding need for such means of 𝐴(𝑡) = 𝐶1 𝑔 + 𝐶2 𝜈𝑒 𝑡(−𝜇−𝜆) – 𝐶3 𝑒 𝑡(− 𝜇− 𝜉) , influence on the relevant target audiences. This 𝐵(𝑡) = − 𝐶1 𝑟 − 𝐶2 𝑢𝑒 𝑡(−𝜇−𝜆) + 𝐶3 𝑒 𝑡(−𝜇− 𝜉) , article is devoted to the statement of a possible 𝐶 (𝑡) = 𝐶1 + 𝐶2 𝑒 𝑡(−𝜇−𝜆) , variant of the decision of the resulted problems. It is known that such problems are solved on 𝐴_0+ 𝐵0 + 𝐶0 𝑢− 𝐶0 𝜈 the basis of modern scientific methods of social where 𝐶1 = , 𝑔−𝑟+𝑢− 𝜈 research theory and information theory. However, − 𝐴0 − 𝐵0 + 𝐶0 𝑔 − 𝐶0 𝑟 𝐶2 = , 𝑔−𝑟+𝑢− 𝜈 recently, research methods have been used, which 𝐴0 𝑟− 𝐴0 𝑢+ 𝐵0 𝑔− 𝐵0 𝜈+ 𝐶0 𝑔𝑢 − 𝐶0 𝑟𝑢 are based on the similarity of the processes of 𝐶3 = , 𝑔−𝑟+𝑢− 𝜈 dissemination of information on social networks and the processes of epidemics [6 − 9]. Therefore, λξ ξ(− λξ+ λ) where g = [ − ], the process of disseminating information on social μ μ(− μ− ξ) 𝜉(− 𝜆𝜉+ 𝜆) networks and viral disease can be analytically 𝜈 = [− 𝜉 + ], 𝜆(𝜆− 𝜉) formalized using the same system of differential (− 𝜆𝜉+ 𝜆) equations. This system of differential equations is 𝑟= , − 𝜇− 𝜉 a mathematical model of the process of (− 𝜆𝜉+ 𝜆) 𝑢= . information dissemination (viral disease) and can 𝜆− 𝜉 be used to optimize the processes of increasing the Data on the quantitative values of the first two potential coverage of the target audience, as well parameters can be obtained by monitoring the as identifying qualitative characteristics of news agent and the number of his subscribers. information that affects the perception of the Parameter ξ takes into account such properties of target audience. This makes it possible to predict the news as the relevance and timing of the reactions of target audiences to a particular publication, as well as the activity of interaction information, i.e., provides an opportunity to of subscribers in the internal networks of the news develop strategies to improve the efficiency of agent. working with the information product, which is Relevance of the news 𝜑 we will interpret as provided to the target audience for its wider the probability of meeting the selected news in all coverage. the sources under consideration. That is 𝑚 Let's move on to a direct consideration of the 𝜑= , 𝑀 analytical model of information dissemination. where 𝑚 – the number of news sources that This model can be represented as the following describe the selected news; system of differential equations [10 -12]: 𝑀 – total number of sources. 𝑑𝐴⁄ = − 𝐴(𝑡)𝜇 + 𝐵 (𝑡)𝜉 + 𝐶 (𝑡)𝜉𝜆; A parameter that characterizes the time of 𝑑𝑡 𝑑𝐵⁄ = − 𝐵 (𝑡)𝜇 − 𝐵(𝑡)𝜉 + 𝐶 (𝑡)𝜆(1 – 𝜉 ); publication of the news 𝛿 визначається 𝑑𝑡 наступним чином: 𝑑𝐶⁄ = (𝐴(𝑡) + 𝐵(𝑡))𝜇 − 𝐶 (𝑡)𝜆. 𝛿 = , 𝑒 { 𝑑𝑡 𝐸 where A – the number of active subscribers to the where 𝑒 – the amount of news on a particular news channel, i.e., those who read the news; topic, which includes controlled news, located in the user's news feed above the control news; 𝐸 – the total amount of news on a specific of growth in the number of subscribers for the topic in the user's news feed. specified time of the study. The next parameter 𝜔 characterizes the The study separately assessed the impact on the probability of users to influence the process of growth of the number of news channel subscribers increasing the readability of news. Let's assume under the following initial conditions of the study: that information and technical capacity of the news 𝑆 channel (its ability to provide news information to a 𝜔 = , (𝐴0 + 𝐵0 ) given population of the study region), socio-political where 𝑆 – the number of users who performed one characteristics of target audiences. as well as the of the actions: like or repost; level of popularity of the selected news channel (𝐴0 + 𝐵0 ) – number of news agent among the population (skill, professionalism of the subscribers. authors of the news, the relevance of the news, the Thus, the probability of reading the news can time of its publication). For each of these initial be given by the following expression: conditions of the study, three variants of news ξ = 𝜑δω. channels were selected, for which the values of all Based on the above, we can conclude that if all necessary parameters of the Table 1 model were the considered parameters of the model are calculated. known, then the values of the function can be calculated 𝐴(𝑡) at the right time and built a schedule Table 1 Parameters of the analytical model of information dissemination № Parameter 𝐴0 𝐵0 𝐶0 𝜆 𝜇 𝜑 δ ω ξ g ν 𝑟 𝑢 𝐶1 𝐶2 𝐶3 Parameter 0,000645 1500000 1300000 1003817 0,00135 0,00399 910081 389925 0,0030 -1,808 -0,367 -0,812 1,714 Version 1 5500 0,90 0,85 value Equation A(t) = 1559879 + 707984e−0,002t − 1003817e−0,00365t 0,00135 0,00064 0,00399 Parameter 850000 800000 536171 263828 534032 0,0030 -1,808 -0,367 -0,812 1,714 Version 2 3000 0,90 0,85 value 5 Equation A(t) = 918997 + 477001e−0,002t − 534032e−0,00365t Parameter 0,000645 0,00135 0,00399 515000 485000 324962 160017 323404 0,0030 -1,808 -0,367 -0,812 1,714 Version 3 1850 0,90 0,85 value Equation A(t) = 556985 + 289310e−0,002t − 323404e−0,00365t So, in fig. 1 shows the results of information dissemination for three information channels of different capacity, able to bring information news to regions with a population of 2.80, 1.65 and 1.00 million people, respectively. It should be emphasized that in order to identify the impact of the information capacity of the channel on the growth of its active subscribers, other parameters of the analytical model for all three news channels under consideration were chosen to be the same. Figure 1: Graphs of growth of the number of subscribers of the news channel according to the information capacity of the channel possible to estimate the required number of such The analysis of the obtained results shows that channels to obtain the desired result of the growth rate of active subscribers of the news information impact on public opinion, taking into channel depends on the number of researched account the population of the studied regions. as target audiences. This is absolutely self-evident well as the popularity of the selected information and logically justified. But the growth of the channel in the area. Thus, to realize the projected number of active subscribers significantly increase in supporters of European integration depends on the relevance of information news, over the next two years through the information political, economic, social orientation of the impact of channels with information capacity and information message, professional skills of its capacity, corresponding to options 1-3, it is presentation, as well as the level of rating necessary at least: authority of the information channel of its energy 3100000: 732000 ≈ 5 information channels capacity and information capacity to disseminate with the capacity of option 1; news. It is clear that these characteristics of the 3100000: 322320 ≈ 10 information channels information channel always have certain with the capacity of option 2; limitations. That is why in order to achieve the 3100000: 194880 ≈ 16 information channels success of the information impact, it is necessary with the ability of option 3. to assess in advance the capabilities of each Thinking similarly, you can calculate the available information channel on the capabilities required number of information and news of its information impact on the growth of the channels targeted at specific target audiences or channel's active subscribers from the total the number of channels of the required level of population. Based on the results of these popularity and quality of information materials. calculations, it is possible to determine the However, it is clear that the qualitative assessment required number of information channels of of information materials, their favorableness, and different information capacity, for example, to i.e., the impact on public opinion during the year achieve the planned positive forecast cannot be equally effective. The success and development of public opinion of the population effectiveness of the information channel depends of Ukraine on accession to the EU. on staffing, training, acquisition, purchase of Thus, from the analysis of the results obtained technical means for the development of materials with the help of the considered analytical model and many other factors. of information dissemination, we can conclude that for the studied period of time (two weeks), for 3. Conclusions the considered variants of the studied population the increase of active subscribers will increase by: The main goal for the system of strategic 1294500 − 1264000 = 30500 new active communications of the Ministry of Defense and subscribers − for option 1; the Armed Forces of Ukraine is to achieve a 875400 − 861970 = 13430 new active strategic narrative. As noted, the positive statistics subscribers − for option 2; of public opinion on support for EU accession is 531010 − 522890 = 8120 new active somewhat reduced, so such a narrative for this subscribers − for option 3. system should be the formation and strengthening That is, with the use of the considered of public opinion on supporting the strategic information channels of the corresponding course of the state. information and technical capacity for the given The application of the proposed mathematical variants of quantitative groups of the population tools to determine the required number of tools the growth of the number of active subscribers (information channels) in the interests of during the year can increase accordingly by: implementing the strategic narrative of the state 30500 * 2 * 12 = 732000 new subscribers; on the basis of analytical model of information 13430 * 2 * 12 = 322320 new subscribers; dissemination, will reasonably form the need and 8120 * 2 * 12 = 194880 new subscribers. scope of information and psychological impact on According to the forecast [2] to ensure the target audiences, and the quality of news desired trends in public opinion in Ukraine, we channels. This will provide an opportunity to need to increase the number of supporters of identify the main tasks for the system of strategic European integration during 2022-2023 by at least communications and realize the interests of the 3.1 million citizens. That is, based on the state in the form of public support for the strategic capabilities of one information channel, it is course of the state to gain full membership of sustainability of the process of development Ukraine in the EU. of public opinion in the implementation of Further development of this study should be the strategic narrative of the state / O.V. carried out on the basis of modern scientific Voitko, V.G. Solonnikov, O.V. 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