In present-day circumstances, social networking services have turned into an effective tool for influencing social and political state processes. As a result of a systematic carrying out of information operations in social networking services, various social movements, which are supported by virtual communities of actors, are appearing. An example of such movements is the negation of effectiveness, safety and legitimacy of vaccination, in particular, mass vaccination. The dissemination and support of the mentioned narrative can threaten not only the informational but also the national security of the state itself. In order to increase the effectiveness of the research on the information confrontation between vaccine proponents and opponents in social networking services, a model of conflict interaction among virtual communities has been proposed. The model includes three layers: the dynamics of the number of two conflicting virtual communities, the growth of the resources of the information space of social networking services connected with the changes in the number of actors in the community, and the dynamics of the consumption of the resources for information confrontation. The suggested approach allows to take into consideration several aspects of the conflicting interaction of virtual communities and also provides a connection between the components of the model using the boundary meaning of the first layer of the model. The simulation results can be used for developing practical recommendations for counteracting the state's information security threats existing in social networking services.
At the present stage of information society development, social networking services
(SNS) have turned into the main source of communication for Internet users.
Currently, SNS such as Facebook, Twitter, Vkontakte, etc. have become the cutting edge
means of organizing communication space and the embodiment of social
communication itself [
An example of the usage of SNS for conducting information confrontation
between the Russian Federation and the United States is the spread of disinformation
containing a strategic anti-vaccination narrative. The research [
The consequence of such systematic information operations in the SNS is the spread of the public movement that denies the effectiveness, safety, and legitimacy of vaccination, in particular, the mass one. The sceptical attitude towards vaccination includes both a complete denial of vaccinations and particular vaccines, which causes a change in the timing and of immunization schedules of the recommended by medical establishments. As a result of the increased anti-vaccine movement in Ukraine and the world in general, the number of patients and fatal cases has increased significantly. On the other hand, this has led to the formation of virtual communities that are opposed to the anti-vaccine movement. The latter is aimed at counteracting the movement of anti-vaccines and are in conflict with its supporters.
A promising area of research is the study of peculiarities of information confrontation of virtual communities aiming to reduce the level of threat to the national security of the state by counteracting destructive content in SNS. Therefore, there is an objective contradiction between ensuring the sustainable development of the SNS information space in the context of globalization and the free circulation of information and lack of effective methodological tools for the investigation of the conflict interaction of virtual communities in order to ensure the information security of the state.
Analysis of recent studies and publications has shown that the solution to the
problem of conflict interaction between supporters and opponents of the anti-vaccine
movement is not properly investigated. Existing studies are limited by the usage of
mathematical models of epidemics, in particular, SIR models [
The purpose of the article is to increase the level of information security of the state in the SNS by modelling the processes of information confrontation of virtual communities of actors, which will allow to develop practical recommendations for counteracting threats in the information space of services. 2 2.1
To identify the signs of conflict of virtual community actors in the SNS, we will
determine the interests of the conflicting parties. The essence of the narrative spread by
pro-vaccination virtual communities in the SNS information can be the following: a
significant reduction of the risk of catching the disease due to conducting the
appropriate vaccinations. According to the World Health Organization, immunization
prevents from 2 to 3 million deaths each year. It is one of the most effective types of
investments in health care in terms of their value [
The interests of the virtual communities that are adherents of the anti-vaccine movement are manifested in the SNS by spreading content with the following narratives: denying the role of vaccination as the factor that reduces the sickness rate; the denial of the necessity of vaccination at present. It is claimed that mass vaccination against all or most of the diseases is inappropriate, since modern treatments for the diseases, which vaccination is carried out from, are effective enough, and the frequency of these diseases themselves is pretty low.
Thus, the essence of the conflict lies in the fact that in real life, SNS actors who oppose vaccination as a result of refusing vaccinations become vulnerable to the disease and also become a threat to those who have been vaccinated. At the same time, the conflict that takes place in the SNS information space influences public opinion in real life and encourages citizens to take certain actions and creates the background for the emergence of threats to the information security and national security of the state as a whole.
Moreover, the considered conflict interaction of virtual communities can be characterised as antagonistic - features intransigence and hostility between groups of actors and manifests in conflict on an ideological basis. 2.2
The modelling of conflict dynamics includes the following points [
In the approach under consideration, three unified modules are used as the components of the models. They describe conflict interaction, increase in and participants’ winnings and losses. Then, the model architecture will be represented as a connected set of three-component models, built on the basis of the same scheme. Such a set of component models contains models of conflict interaction of virtual communities that describe the movement of conflict elements and their relationships; virtual community benefit models that describe the effects of conflict interaction; models of expenditures of virtual communities on information confrontation; connection of models of winnings and costs of virtual communities with conflict model.
The conflict is that the gain of one virtual community is equal to the loss of another, or the increase in the number of supporters of vaccination is associated with a decrease in the number of supporters of the anti-vaccination movement. where x(t) , y(t) – the number of actors of opposing virtual communities in the SNS information space; a , b – parameters of conflict interaction; u , v – control parameters.
The component of the model describes the gains of the virtual community as a result of conflict engagement as the growth of the certain resource associated with interests that are the cause of the conflict. In particular, such a resource is a portion of the SNS information space that is formed directly by the actor-carrier of the given narrative. The payoff model can be considered as assessment of the efficiency of conflict interaction for determination of the function of conflict effectiveness dx(t) dyd(tt) dt f x(t),a,u, f y(t),b, v; dsd(tt) dt dr(t) f r(t),c, u, f s(t), d , v; (1) (2) where r(t) , s(t) – the variables that characterize the gain growth – the part of the SNS information space formed and controlled by the virtual community actors; c , d – parameters of conflict interaction of virtual communities in SNS; u , v – control parameters.
The cost model formalizes the growth of some cost-related resource that accompanies the conflict of virtual communities in the SNS information space. Such a resource is the cash costs spent on trolls’ payments, time outlay used to achieve the goal of the conflict, the cost of technical support for conducting information war, etc. The expenditure model can also be seen as a characteristic for assessing conflict interaction to determine the effectiveness of conducting the information confrontation in SNS. In general, it takes the following form dpd(tt) f p(t), g, u , dq(t) f q(t), h, v; dt (3) where p(t) , q(t) – variables that characterize the costs of conflict interaction of virtual communities; g , h – parameters of interaction in SNS; u , v – control parameters.
As a result, the chosen model allows to simulate the processes of information
confrontation of virtual communities on the example of antagonistic conflict in the SNS
information space by varying the parameters of the three-layer model. It is advisable
to present the developed conceptual model as a structural diagram, the form of which
is shown in Fig. [
u …
r(t) SNS
VC1 … p(t) … … x(t) a, c, g b, d, h q(t) … … y(t)
v s(t)
… …
VC2 by b , d , h for the second group of actors. As the result of the change of these parameters, the number of actors in the corresponding virtual communities x t and y t also changes. This causes the changes of the resources of the communities of actors r t and s t . In this case, the amount of resources spent on conducting counter-party information operations in the SNS is determined by the functions p t and q t . Control vectors u and v for virtual communities provide the change of the parameters of conflict interaction according to a certain law.
Thus, the structural models of the parties of the conflict contain three components each and take the following form: the model of virtual community 1 the model of virtual community 2 dxd(tt) f x(t),a,u, dr(t) dt f r(t),c,u, dp(t) f p(t), g,u; dt dyd(tt) ) f y(t),b, v, ds(t) f s(t),d , v, dt dq(t) f q(t),h, v.
dt 2.3
The choice of the type of differential equation of the dynamics of information
confrontation of virtual communities is an important issue from the point of view of the
study of conflict interaction in the SNS information space. Let us choose the function
of limited growth to formalize the conflict interaction of virtual community actors,
which combines accelerated growth in the initial phase and accelerated deceleration in
the final phase of antagonistic conflict. Such kind of differential equation includes
control parameters [
There is some characteristic value W for solving the differential growth equation wt , for which all components of expression (6) become zero at d 2wt
The value W / a0 is called the threshold of the function of limited growth, to which the values of the state variables at large values of the time interval direct asymptotically. Thus W – is a characteristic parameter of the function of limited growth that physically determines some limit value that studied value can reach.
From general equation (6) we can obtain partial cases, among which we emphasize
those that have a threshold character [
All growth equations are characterized by a common element (a0wt )
used to determine the threshold. Since the logistic equation is a particular case of the
differential growth equation (6), the equilibrium region of the growth equation is valid
for it. Although for the implementation of component models (1) – (3) any equations
in Table [
dt
The threshold of the function of limited growth W is considered as a parametrically dependent value. The solution of this differential equation is the function of (7) (8) growth of the investigated value, which is a description of the conflict of virtual communities in the SNS. 2.4
Let's present separate layers of the equation of the model of conflict dynamics based
on the limited growth of the first order [
x t X y t Y
1 x t 0, 1 y t 0; where a , b – the parameters that prevent the increase in the number of actors of the corresponding virtual communities in the SNS; , – exponential growth indicators contributing to the growth of the number of actors; X , Y – limit values of the number of actors of opposing virtual communities.
For curves that describe limited growth, characteristic parameters X / a and Y / b that limit the growth in the number of actors in the respective virtual communities are important. The conflict of actors is manifested in the fact that their total number is considered to be constant x(t) y(t) n(t) const, X (t) Y (t) N(t) const , and each virtual community tries to increase its number; 2. The second layer of the model formalizes the growth of resources r t and s t – corresponding benefits of virtual communities 1 cr t 1 ds t dr t
dt ds t dt
r t R s t S
1 r t 0, 1 s t 0; where c , d – parameters that adversely affect the level of winnings resulting from information confrontation in the SNS; , – exponential growth rates of gain; R , S – thresholds for the winnings of virtual communities.
For curves, the characteristic parameter that limits the gain growth R / c , S / d is important. In this case, the limit values of the resources r t and s t depend on the threshold values of the number of actors of virtual communities in SNS x t , y t . At the same time the amount of winnings is not constant, which is connected with the non-deterministic behaviour of the actors in the SNS information space. 3. The third layer of the model characterizes the dynamics of resource expenditures for information confrontation in SNS 1 gp t 1 hq t dp t
dt dq t dt
p t P q t Q
1 p t 0, 1 q t 0; (11) where g , h – the parameters that negatively affect the cost level; , – intensity of expenditures for conducting operations (exponential growth rates); P , Q – the maximum amount of resources allocated for conducting the conflict P / g , Q / h . The amount of resources spent on information warfare is also variable. 2.5
Resource limits r(t) and s(t) depend on the thresholds of the number of actors x(t) , y(t) . In simple cases, we restrict ourselves to a linear dependence in the form R X , S Y . At the same time, resource limit values depend on the thresholds values of the number of virtual communities actors involved in the conflict S f (Y ) , R f (X ) , P f (X ) , Q f (Y ) .
The nature of communication depends on the investigated aspect of the subject area. In simple cases, it is possible to limit ourselves to a linear dependence of the form S Y , R X that sets the scale of the output function. For linear dependence, there may occur difficulties connected with the decrease of the value of the function y f (t,u,v) in time. Let’s assume that as the number of actors of the virtual community in a state of conflict decreases, then the winnings and resources of this community in the management of information warfare also decreases. Suppose that these quantities will vary in a complex way, which is related to the inverted S-shaped nature of the function y f (t,u,v) and the requirement to fulfill the condition x y z . However, a non-inverted S-function must be used to describe the benefits and expenditure of resources. To resolve this discrepancy, we use the following technique.
As a function of movement of gained resources and expense of resources we will use the functions of the limited growth with a variable value of a threshold, where the current values of the function of the original are used as the threshold, i.e. R f (x) , S f ( y) , P f (x) , Q f ( y) . Such dependence of threshold values is algorithmic and can be considered as a way of parametric control of movement of resources. Such functions can be convex in nature, which distinguishes them from the classic Sshaped features that have a monotonous growth pattern. Thereby, the constrained growth functions with a variable threshold value describes the relationship with the inverse S-function more adequately. 3
To implement the computational experiment, we write the first layer of the model of antagonistic conflict of virtual communities in the SNS information space (9) in the form of a system of recurrent equations 1 xk xk 1 1 X xk , 1 axk 1 yk yk 1 1 Y yk , 1 byk xk yk nk , X Y N. (12) The limit values of the numbers of virtual communities of supporters X and opponents Y of vaccination are considered as desirable values of the number of carriers of a certain narrative as a result of conducting information confrontation in the SNS. We write the layers (10) – (11) in the form of recurrent formulas similarly to the expression (12).
The results of a study [25] showed that a rigid stance against vaccinations is supported only by a small number of parents, whereas various forms of “vaccine scepticism” and uncertainty about the need for vaccination are more widely spread. Less than 2% of parents fully reject vaccination, while selective or late vaccination is practiced by 2% to 27% of parents. “Vaccine hesitant” are from 20% to 30% of parents [25].
To conduct computational experiment, let us consider the situation where the
number of actors in SNS who oppose vaccination has reached the critical mark of 30%
the value that precedes the start of the epidemic. To reduce the threat of the epidemic,
let’s consider the following scenario: as a result of preventive work, in particular in
the SNS information space, the number of vaccine opponents is reduced to 5%, and
the number of vaccination supporters is increased to 95% (Fig. [
The speed of change depends on the values of the control parameters a and b which are determined by the level of unacceptance by the actors of the relevant virtual communities of the narrative concerning the importance of early vaccination in order to prevent epidemics. It is possible to reduce the value of these parameters by transferring information to the virtual anti-vaccine community in an accessible form in order to influence their public opinion. The resulting values of the number of actors who are supporters and opponents of vaccination will be used as the current value of the conflict interaction function.
Fig. 2. Change in the number of supporters x(t) and opponents y(t) of vaccination to prevent epidemics at the following parameter values: 1 – a 0 and b 0 ; 2 – a 0,01 and b 0,01 ; 3 – a 0,02 and b 0,02
Fig. 4. Dynamics of resource expenditures q(t) (curves 1–3) for h 0,02;0,01;0 and benefit
s(t) (curves 4–6) d 0,02;0,01;0 for the virtual community of vaccination advocates
Dependencies are described by convex curves, which is explained by the use of
variable growth functions with variable thresholds. Also Fig. [
A three-layer model of conflict interaction of virtual communities in the SNS information space has been presented. It allows to formalize the processes of information confrontation on the example of the social anti- vaccination movement. The first layer of the model is used to formalize the conflict itself - the redistribution of actors between virtual communities as a result of conducting information operations. The second layer is intended to reflect the gain - the amount of SNS information resource that is controlled by the virtual community actors as a result of increasing the number of its actors. The third layer describes the expenditure of the resources for direct information combat in the SNS information space.
Each layer represents two differential equations that define the functions of limited growth for a particular aspect of the conflict interaction of virtual communities. The main characteristic parameter of such functions is the asymptotic threshold used to relate the equations to the system. The thresholds of winnings and losses functions depend on the thresholds of the functions describing the conflicting interaction of virtual communities. In this case, a variable-threshold approach is used for the winnings and losses functions. As the threshold value we use the current value of the conflict interaction function. The results of the modelling of conflict interaction of virtual communities in SNS allow to increase the effectiveness of the research of information confrontation processes and to develop effective measures to counter the threats to the information security of the state. 25. Leask, J., Kinnersley, P., Jackson, C., Cheater, F., Bedford, H., Rowles, G.: Communicating with parents about vaccination: a framework for health professionals. BMC pediatrics 12 pp. 154 (2012). doi:10.1186/1471-2431-12-154