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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Determining the Required Number of Information Channels Based on the Information Dissemination Model</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Oleksandr Voitko</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Volodymyr Cherneha</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Vladislav Solonnikov</string-name>
          <email>vladislavsolonnikov@ukr.net</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Olena Poliakova</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Roman Korolyov</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Simon Kuznets Kharkiv National University of Economics</institution>
          ,
          <addr-line>Kharkiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>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.</p>
      </abstract>
      <kwd-group>
        <kwd>1 Target audience</kwd>
        <kwd>narrative</kwd>
        <kwd>dissemination of information</kwd>
        <kwd>strategic communications</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Ukraine's integration into the Euro-Atlantic
security space and the acquisition of NATO
membership have been identified as the main goal
of Ukraine's Military Security Strategy, which
was enacted by the Decree of the President of
Ukraine in March 2021. To achieve this goal,
Ukraine will take a set of appropriate measures.
One such measure is countering in cyberspace and
imposing one's will in the information space [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
      </p>
      <p>To organize the implementation of such a task,
it is necessary to have an effective and efficient
system of strategic communications of the state,
which uses a single information space, has reliable
channels of communication with the population
and an appropriate branched information
infrastructure.</p>
    </sec>
    <sec id="sec-2">
      <title>2. General Problem Statement</title>
      <p>
        In previous publications, the authors solved the
problem of scientific substantiation of accession
to the EU, NATO on the basis of analysis of
statistical data of public opinion and forecasting
scenarios for its development [
        <xref ref-type="bibr" rid="ref2 ref3">2, 3</xref>
        ].
      </p>
      <p>The obtained forecast data allowed to
determine the peculiarities of the implementation
of the strategic narrative of the state by the system
of strategic communications and to realize the
interests of the state in the form of public support
for its strategic course to Ukraine's full
membership in the EU and NATO. The proposed
approach will allow to develop effective and
efficient materials of information and
psychological impact, which will be implemented
by a system of strategic communications when
influencing the relevant target audiences. An
extremely important task will be to study the
processes that characterize the distribution of
information materials, as well as the 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. This article is devoted to the
statement of a possible variant of the decision of
the resulted problems.</p>
    </sec>
    <sec id="sec-3">
      <title>2.1. Analysis of recent research and publications</title>
      <p>The armed aggression of the Russian
Federation against Ukraine is carried out in
various directions of the "hybrid war". Aggressive
influences are carried out both simultaneously and
consistently, practically on all spheres of life of
the state, thus the received results in one sphere
are at once used for strengthening of influence in
other spheres. To date, a large number of domestic
and foreign scientists are engaged in research on
"hybrid actions". In the works of Landa D.V.,
Danyka Y.G., Salnikova O.F., Snitsarenko P.M.
and many others, covers materials on the forms
and methods used by the aggressor to achieve its
imperial goals, and contains a number of
theoretical provisions, recommendations on
possible ways to counter. Unfortunately, scientific
publications on the mathematical justification of
the necessary forces and means, in achieving
specific goals, are not enough.</p>
      <p>
        A number of software services are available on
the Internet, with which it is possible to simulate
the process of information dissemination. The
authors with the help of one of such services
(Melting Asphalt) visualized a model of
information dissemination among the target
audience [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. Indicators that influence the
dissemination of information among target
audiences are proposed, and a visualization of the
information dissemination model is developed
[
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
      </p>
      <p>The purpose of the article is the development
of 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 process of
dissemination of information.</p>
    </sec>
    <sec id="sec-4">
      <title>2.1.1. Research results</title>
      <p>Today, along with Ukraine, there are several
states and their associations, more powerful than
Ukraine, which have interests different from the
national interests of Ukraine, and Ukraine is not
able to resist their aggressive actions alone.
Therefore, joining NATO is one of the
government's priorities in order to protect national
interests.</p>
      <p>Public opinion gained very drastic changes in
the direction of European and North Atlantic
cooperation with the beginning of the armed
aggression of the Russian Federation.
Unfortunately, during the war, Ukrainian society
did not get the desired result in terms of proper
support and national security of Ukraine from the
EU and NATO. Starting in 2017, the number of
supporters of such integration began to gradually
decrease.</p>
      <p>
        Public opinion on EU accession has changed
somewhat depending on the political, military and
economic processes that have taken place in
Ukraine over the past two decades. To achieve the
stated goal of the study, it is not enough for us to
assess only the current distribution of public
opinion on this issue. It is necessary to identify the
general trends of its change in the future, to
choose those that are directed in the desired
direction for us and are characterized by the
greatest reliability. This was achieved using
scientific forecasting, namely the method of
statistical extrapolation. The analysis of the
obtained results shows that in order to ensure
further positive forecast development of public
opinion of the population of Ukraine on EU
accession it is necessary in 2022 and 2023 to
increase the number of supporters of society in
this direction by 2.4 million people, respectively.
(6.3%) in 2022 and 0.7 million people. (2.1%) in
2023 [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>The obtained forecast data provided an
opportunity to determine the peculiarities of the
implementation of the strategic narrative of the
state by the system of strategic communications
and to realize the interests of the state in the form
of public support for its strategic course to
Ukraine's full membership in the EU and NATO.
An extremely important task will be to study the
processes that characterize the distribution of
information materials, as well as the 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. In order to calculate the
required number of information channels that will
be used in the implementation of the strategic
narrative of the state, it is necessary to calculate
the
corresponding
need for such
means
of
influence on the relevant target audiences. This
article is devoted to the statement of a possible
variant of the decision of the resulted problems.</p>
      <p>
        It is known that such problems are solved on
the basis of modern scientific methods of social
research theory and information theory. However,
recently, research methods have been used, which
are based on the similarity of the processes of
dissemination of information on social networks
and the processes of epidemics [
        <xref ref-type="bibr" rid="ref6 ref7 ref8 ref9">6 − 9</xref>
        ]. Therefore,
the process of disseminating information on social
networks and viral disease can be analytically
formalized using the same system of differential
equations. This system of differential equations is
a
mathematical
model
of
the
process
of
information dissemination (viral disease) and can
be used to optimize the processes of increasing the
potential coverage of the target audience, as well
as
identifying
qualitative
characteristics
of
information that affects the perception of the
target audience. This makes it possible to predict
the reactions of target audiences to a particular
information, i.e., provides an opportunity to
develop strategies to improve the efficiency of
working with the information product, which is
provided to the target audience for its wider
coverage.
      </p>
      <p>
        Let's move on to a direct consideration of the
analytical model of information dissemination.
This model can be represented as the following
system of differential equations [
        <xref ref-type="bibr" rid="ref10 ref11 ref12">10 -12</xref>
        ]:
      </p>
      <p>= −  ( ) +  ( ) +  ( ) ;
= −  ( ) −  ( ) +  ( ) (1 –  );</p>
      <p>= ( ( ) +  ( )) −  ( ) .
{
where A – the number of active subscribers to the
news channel, i.e., those who read the news;
B – the number of inactive subscribers to
the channel, i.e. those who have not read the news,
but are subscribers;
did not read the news;
agent;
news agent;</p>
      <p>C – the number of non-subscribers who
λ – the intensity of subscribing to a news
μ – the intensity of unsubscribing from the
ξ – intensity of reading the news.</p>
      <p>With the initial conditions at the time  = 0:
 (0) =  0,  (0) =  0,  (0) =  0.</p>
      <p>0 &gt; 0,  0 &gt; 0,  0 &gt; 0.</p>
      <p>The solution of this system of equations can be
presented as follows:</p>
      <p>( ) =  1 +  2    (− − ) –  3   (−  −  ),
 ( ) = −  1 −  2    (− − ) +  3
  (− −  ) ,
 ( ) =  1 +  2  (− − ),
where  1 =
 _0+  0 +  0  −  0  ,</p>
      <p>− + − 
 2 = −  0 −  0 +  0 −  0  ,</p>
      <p>− + − 
 3 =
 0 −  0
 +  0 −  0 +  0</p>
      <p>−  0 
 − + − 
where g = [
λξ
μ
− ξ(− λξ+ λ)],</p>
      <p>μ(− μ− ξ)
 = [−  +
 = (−  +  ),</p>
      <p>−  − 
 = (−</p>
      <p>+  ).
 − 
 (− 
 ( −  )</p>
      <p>+  )],</p>
      <p>Data on the quantitative values of the first two
parameters can be obtained by monitoring the
news agent and the number of his subscribers.
Parameter ξ takes into account such properties of
the
news as the
relevance
and timing
of
publication, as well as the activity of interaction
of subscribers in the internal networks of the news
agent.</p>
      <p>Relevance of the news  we will interpret as
the probability of meeting the selected news in all
the sources under consideration. That is
 =
where</p>
      <p>– the number of news sources that
describe the selected news;</p>
      <p>– total number of sources.</p>
      <p>A parameter that characterizes the time of




publication</p>
      <p>of
наступним чином:
the
news</p>
      <p>визначається
 = ,
where  – the amount of news on a particular
topic, which includes controlled news, located in
the user's news feed above the control news;</p>
      <p>The analysis of the obtained results shows that
the growth rate of active subscribers of the news
channel depends on the number of researched
target audiences. This is absolutely self-evident
and logically justified. But the growth of the
number of active subscribers significantly
depends on the relevance of information news,
political, economic, social orientation of the
information message, professional skills of its
presentation, as well as the level of rating
authority of the information channel of its energy
capacity and information capacity to disseminate
news. It is clear that these characteristics of the
information channel always have certain
limitations. That is why in order to achieve the
success of the information impact, it is necessary
to assess in advance the capabilities of each
available information channel on the capabilities
of its information impact on the growth of the
channel's active subscribers from the total
population. Based on the results of these
calculations, it is possible to determine the
required number of information channels of
different information capacity, for example, to
achieve the planned positive forecast
development of public opinion of the population
of Ukraine on accession to the EU.</p>
      <p>Thus, from the analysis of the results obtained
with the help of the considered analytical model
of information dissemination, we can conclude
that for the studied period of time (two weeks), for
the considered variants of the studied population
the increase of active subscribers will increase by:
1294500 − 1264000 = 30500 new active
subscribers − for option 1;</p>
      <p>875400 − 861970 = 13430 new active
subscribers − for option 2;</p>
      <p>531010 − 522890 = 8120 new active
subscribers − for option 3.</p>
      <p>That is, with the use of the considered
information channels of the corresponding
information and technical capacity for the given
variants of quantitative groups of the population
the growth of the number of active subscribers
during the year can increase accordingly by:
30500 * 2 * 12 = 732000 new subscribers;
13430 * 2 * 12 = 322320 new subscribers;
8120 * 2 * 12 = 194880 new subscribers.</p>
      <p>
        According to the forecast [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ] to ensure the
desired trends in public opinion in Ukraine, we
need to increase the number of supporters of
European integration during 2022-2023 by at least
3.1 million citizens. That is, based on the
capabilities of one information channel, it is
possible to estimate the required number of such
channels to obtain the desired result of
information impact on public opinion, taking into
account the population of the studied regions. as
well as the popularity of the selected information
channel in the area. Thus, to realize the projected
increase in supporters of European integration
over the next two years through the information
impact of channels with information capacity and
capacity, corresponding to options 1-3, it is
necessary at least:
      </p>
      <p>3100000: 732000 ≈ 5 information channels
with the capacity of option 1;</p>
      <p>3100000: 322320 ≈ 10 information channels
with the capacity of option 2;</p>
      <p>3100000: 194880 ≈ 16 information channels
with the ability of option 3.</p>
      <p>Thinking similarly, you can calculate the
required number of information and news
channels targeted at specific target audiences or
the number of channels of the required level of
popularity and quality of information materials.
However, it is clear that the qualitative assessment
of information materials, their favorableness, and
i.e., the impact on public opinion during the year
cannot be equally effective. The success and
effectiveness of the information channel depends
on staffing, training, acquisition, purchase of
technical means for the development of materials
and many other factors.</p>
    </sec>
    <sec id="sec-5">
      <title>3. Conclusions</title>
      <p>The main goal for the system of strategic
communications of the Ministry of Defense and
the Armed Forces of Ukraine is to achieve a
strategic narrative. As noted, the positive statistics
of public opinion on support for EU accession is
somewhat reduced, so such a narrative for this
system should be the formation and strengthening
of public opinion on supporting the strategic
course of the state.</p>
      <p>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
scope 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 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.</p>
      <p>Further development of this study should be
carried out on the basis of modern scientific
methods of the theory of social research and the
theory of information operations in order to
identify time indicators that characterize the
distribution of materials of information influences
to each target audience. It is especially important
to receive such information from the temporarily
occupied territories of Donetsk and Luhansk
regions, as well as the Autonomous Republic of
Crimea, which will allow to reasonably identify
target audiences, argue the subject of messages
and channels of information and psychological
influence. To ensure the optimal total information
impact, it is advisable to carry out a scientifically
sound distribution of the projected total volume of
tasks between the various structural units of the
system of strategic communications, taking into
account the characteristics of different target
audiences. This will provide an opportunity not
only to specify the goals and objectives for each
structural unit of the strategic communications
system, but also to develop effective and efficient
materials of information and psychological
impact to achieve them. This will allow to argue
the subject of messages and choose the channels
of distribution of materials of information and
psychological influence, taking into account the
individual characteristics of target audiences.</p>
      <p>Reviewer: Doctor of tech. sciences. Professor
Evseev S.P., Head of the Department of
Cybersecurity and Information Technology,
S. Kuznets Kharkiv National University of
Economics.</p>
    </sec>
    <sec id="sec-6">
      <title>4. References</title>
    </sec>
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