247 ISSN 1064-5624, Doklady Mathematics, 2018, Vol. 97, No. 3, pp. 247–249. © Pleiades Publishing, Ltd., 2018. Original Russian Text © A.P. Mikhailov, A.P. Petrov, G.B. Pronchev, O.G. Proncheva, 2018, published in Doklady Akademii Nauk, 2018, Vol. 480, No. 4, pp. 397–400. Modeling a Decrease in Public Attention to a Past One-Time Political Event A. P. Mikhailov a, *, A. P. Petrov a, **, G. B. Pronchev b, ***, and O. G. Proncheva a,c, **** Presented by Academician of the RAS B.N. Chetverushkin July 7, 2017 Received February 7, 2018 Abstract—A model is introduced that describes a decrease in public attention to a past one-time political event, such as one-round elections, referendums, and coup d'état attempts. The number of web search queries is taken as an empirical measure of public attention to the event. The model is shown to match actual data. DOI: 10.1134/S1064562418030158 FORMULATION OF THE PROBLEM Empirical studies show that public attention to one-time political events, such as referendums, one- round elections, and failed coups, is maximum on the day of appearing crucial information on an event and then decreases over time. By crucial information, we mean announcements of election or referendum results or coup announcements. In terms of measurement, a convenient character- istic of public attention to an event is the number of web search queries about the event that users enter into a web search engine. Methods based on the linguistic analysis of web search queries are well elaborated and applied in Internet sociology (see, e.g., [1, 2]). To the best of our knowledge, there are no models describing the dynamics of web search query numbers. The goal of this study is to construct a mathemati- cal model describing the empirical dynamics of the number of web search queries concerning a one-time event. The practical value of this problem formulation is associated with the importance of predictions of social situations developing after certain events. For example, models of information warfare in society [3–6] either do not take into account a decrease in public attention with time at all or use the factor of forgetting information, which was introduced on the basis of general considerations and was not supported by empirical data. The basic empirical finding is that, immediately after a one-time political event, the number of queries about it is reduced much faster than exponentially. More specifically, the number of queries is well approximated by the function . Thus, the task of this work is to develop a model describing such dynamics. CONSTRUCTION OF THE MODEL Let denote time and be the moment of appearance of crucial information. The model is based on Rashevsky’s neurological scheme [7–9], which assumes that the response of an individual is deter- mined by two factors. One of them is a fundamental intrinsic factor (remaining unchanged in the consid- ered process) that accumulates previous experience of the individual and his or her social position in the form of political (and other) views. The other is the dynam- ical factor of public attention to a given political event; it varies in the considered process under the influence of informational stimuli received from the social envi- ronment. The basic behavioral hypothesis is that an individ- ual responds in a certain way on a particular day (in the given model, makes a web search query about a polit- ical event) if the sum of the intrinsic and dynamical factors exceeds a threshold value h. The intrinsic factor of an individual is character- ized by the quantity reflecting his or her general interest in political events of the given type: cor- responds to the lack of interest. The individual distri- - exp[exp( )] t t =0 t ϕ≥ 0 ϕ =0 MATHEMATICS a Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia b Faculty of Sociology, Moscow State University, Moscow, 119992 Russia c Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700 Russia *e-mail: apmikhailov@yandex.ru **e-mail: petrov.alexander.p@yandex.ru ***e-mail: pronchev@rambler.ru ****e-mail: olga.proncheva@gmail.com