Impact of Propagation Information in the Model of Tax Audit

  • Elena GubarEmail author
  • Suriya Kumacheva
  • Ekaterina Zhitkova
  • Olga Porokhnyavaya
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)


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 even selective tax audits are not always profitable. In this case the propagation of information can be viewed as an “infection of the mind,” and its spread shows an interesting resemblance to that of epidemics. We thus use a modification of the classical Susceptible-Infected-Recovery model to describe the process. We assume that information propagates through the population by pairwise contacts between spreaders and others in the population and Informed agents disseminate information through their network of contacts or social networks. We study a model of spreading information in a large population of taxpayers and describe the dynamics of this process in complex social networks. We formulate an optimal control problem of tax auditing and analyze the behavior of agents in different subgroups depending on received information.


Tax control Information spreading SIR model Epidemic process Optimal control Social networks 


  1. 1.
    Bure, V.M., Kumacheva, S.Sh.: A game theory model of tax auditing using statistical information about taxpayers. Vestnik SPbGU, series 10, vol. 4, pp. 16–242 (2010) (in Russian)Google Scholar
  2. 2.
    Federal State Statistics Service: The web-site of the Russian Federation State Statistics Service (2015). Available:
  3. 3.
    Goffman, W., Newill, V.A.: Generalization of epidemic theory: an application to the transmission of ideas. Nature 204 (4955), 225–228 (1964)CrossRefGoogle Scholar
  4. 4.
    Gubar, E.A., Zhu, Q.: Optimal control of influenza epidemic model with virus mutations. In: 12th Biannual European Control Conference (ECC 13), pp. 3125–3130. IEEE Control Systems Society, Zurich (2013)Google Scholar
  5. 5.
    Gubar, E.A., Zhitkova, E.M., Kupchinenko, E.M., Petriakova, N.S.: Two modes of vaccination program in controlled SIR model. In: L.A. Petrosyan, N.A. Zenkevich (eds.) Contributions of the 8th International Conference GTM 2012, pp. 84–98 (2015)Google Scholar
  6. 6.
    Gubar, E.A., Kumacheva, S.Sh., Zhitkova, E.M., Porokhnyavaya, O.Yu.: Propagation of information over the network of taxpayers in the model of tax auditing. In: Stability and Control Processes in Memory of V.I. Zubov SCP 2015, IEEE Conference Publications, pp. 244–247 (2015). INSPEC Accession Number: 15637330Google Scholar
  7. 7.
    Fu, X., Small, M., Walker, D.M., Zhang, H.: Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization. Phys. Rev. E 77, 036113 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kandhway, K., Kuri, J.: Optimal control of information epidemics modeled as Maki Thompson rumors. Commun. Nonlinear Sci. Numer. Simul. 19 (12) (2014)Google Scholar
  9. 9.
    Kendall, M.G., Stuart, A.: Distribution Theory. Nauka, Moscow (1966) (in Russian)zbMATHGoogle Scholar
  10. 10.
    Kermack, W.O., Mc Kendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. Ser. A 115 (A771), 700–721 (1927)CrossRefzbMATHGoogle Scholar
  11. 11.
    Khouzani, M.H.R., Sarkar, S., Altman, E.: Optimal control of epidemic evolution. In: Proceedings of IEEE INFOCOM (2011)CrossRefGoogle Scholar
  12. 12.
    Kumacheva, S.Sh., Gubar, E.A.: Evolutionary model of tax auditing. In: Contributions to Game Theory and Management, vol. 8, pp. 164–175 (2015)MathSciNetGoogle Scholar
  13. 13.
    Nekovee, A.M., Moreno, Y., Bianconi, G., Marsili, M.: Theory of rumor spreading in complex social networks. Physica A 374, 457–470 (2007)CrossRefGoogle Scholar
  14. 14.
    Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86 (14), 3200–3203 (2001)CrossRefGoogle Scholar
  15. 15.
    Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F.: The Mathematical Theory of Optimal Processes. Interscience, New York (1962)Google Scholar
  16. 16.
    Porokhnyavaya, O.Yu.: One algorithm for constructing a scale-free networks. In: Control Processes and Stability, vol. 2, issue 18, pp. 702–707 (2015)Google Scholar
  17. 17.
    Reinganum, J.R., Wilde, L.L.: Income tax compliance in a principal–agent framework. J. Publ. Econ. 26, 1–18 (1985)CrossRefGoogle Scholar
  18. 18.
    Sanchez, I., Sobel, J.: Hierarchical design and enforcement of income tax policies. J. Publ. Econ. 50, 345–369 (1993)CrossRefGoogle Scholar
  19. 19.
    Vasin, A.A., Vasina, P.A.: The optimization of tax system in condition of tax evasion: the role of penalty restriction. M., EERC (2002) (in Russian)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Elena Gubar
    • 1
    Email author
  • Suriya Kumacheva
    • 1
  • Ekaterina Zhitkova
    • 1
  • Olga Porokhnyavaya
    • 1
  1. 1.Faculty of Applied Mathematics and Control ProcessesSt. Petersburg State UniversitySt. PetersburgRussia

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