Advertisement

Modeling the effect of information transmission on the drug dynamic

  • Reza MemarbashiEmail author
  • Elahe Sorouri
Regular Article

Abstract

In each community, there is a lot of information about the disadvantages and risks of drug use and its negative effects on health, work, honor, and other living funds of people. A group of individuals, who can be called responsive individuals, will be safe from the risk of drug abuse, by receiving and understanding such information. In this paper, by proposing mathematical models, we investigate the effect of the distribution of this kind of information on the transformation of susceptible individuals into responsive individuals as well as their effect in preventing the occurrence of substance abuse epidemics. In these models, we take into account the fact that the spirit of responsiveness of these individuals can be decayed with time, and these people can become susceptible people, and eventually to addicts. We analyze the dynamical properties of the models, such as local and global stability of equilibrium points and the occurrence of backward bifurcation. The results of this study show that the higher the rate of conversion of susceptible individuals to those responsive, the prevention of drug epidemy is easier.

References

  1. 1.
    J. Arino, C.C. McCluskey, P. van den Driessche, SIAM J. Appl. Math. 64(1), 260 (2003)MathSciNetCrossRefGoogle Scholar
  2. 2.
    B. Buonomo, D. Lacitignola, Note di Mate. 30(2), 83 (2011)Google Scholar
  3. 3.
    B. Buonomo, A. d’Onofrio, D. Lacitignola, Math. Bios. 216(1), 9 (2008)CrossRefGoogle Scholar
  4. 4.
    C. Castillo-Chavez, B. Song, Math. Biosci. Eng. 2, 361 (2004)CrossRefGoogle Scholar
  5. 5.
    J. Cui, Y. Sun, H. Zhu, J. Dyn. Differ. Equ. 20, 31 (2008)CrossRefGoogle Scholar
  6. 6.
    A. D’Onfrio, P. Manfredi, J. Theor. Biol. 256, 473 (2009)CrossRefGoogle Scholar
  7. 7.
    B. Dubeya, P. Dubeya, U.S. Dubeyb, Nonlinear Anal. Model. Control 21(2), 185 (2016)Google Scholar
  8. 8.
    B. Fang, X.Z. Li, M. Martcheva, L.M. Cai, Appl. Math. Comput. 263, 315 (2015)MathSciNetGoogle Scholar
  9. 9.
    A.B. Gumel, C.C. McCluskey, J. Watmough, Math. Biosci. Eng. 3, 485 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    A.S. Kalula, F. Nyabadza, S. Afr. J. Sci. 108(3–4), 1 (2012)Google Scholar
  11. 11.
    I.Z. Kiss, S. Cassell, M. Ricker, P.L. Simon, Math. Biosci. 225, 1 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    M.Y. Li, J.S. Muldowney, SIAM J. Math. Anal. 27(4), 1070 (1996)MathSciNetCrossRefGoogle Scholar
  13. 13.
    M.Y. Li, J.S. Muldowney, Rocky Mt. J. Math. 25(1), 365 (1995)CrossRefGoogle Scholar
  14. 14.
    W.M. Liu, S.A. Levin, Y. Iwasa, J. Math. Biol. 23, 187 (1986)MathSciNetCrossRefGoogle Scholar
  15. 15.
    M. Lizana, J. Rivero, J. Math. Biol. 35, 21 (1996)MathSciNetCrossRefGoogle Scholar
  16. 16.
    M. Martcheva, An Introduction to Mathematical Epidemiology (Springer, Berlin, 2015)CrossRefGoogle Scholar
  17. 17.
    Z. Mukandavire, W. Garira, J.M. Tchuenche, Appl. Math. Model. 33(4), 2084 (2009)MathSciNetCrossRefGoogle Scholar
  18. 18.
    G. Mulone, B. Straughan, Math. Biosci. 218(2), 138 (2009)MathSciNetCrossRefGoogle Scholar
  19. 19.
    H.J.B. Njagarah, F. Nyabadza, J. Biol. Syst. 21(1), 135 (2013)CrossRefGoogle Scholar
  20. 20.
    F. Nyabadza, J.B. Njagarah, R.J. Smith, Bull. Math. Biol. 75(1), 24 (2013)MathSciNetCrossRefGoogle Scholar
  21. 21.
    F. Nyabadza, S.D. Hove-Musekwa, Math. Biol. 225(2), 132 (2010)Google Scholar
  22. 22.
    G.P. Samanta, J. Appl. Math. Comput. 35(1–2), 161 (2011)MathSciNetCrossRefGoogle Scholar
  23. 23.
    B. Thurman, J. Boughelaf, Drugs Alcohol Today 15(3), 127 (2015)CrossRefGoogle Scholar
  24. 24.
    UNODC, International standards on drug prevention. UNODC, New York, (2013)Google Scholar
  25. 25.
    E. White, C. Comiskey, Math. Biosci. 208(1), 312 (2007)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Y.N. Xiao, T.T. Zhao, S.Y. Tang, Math. Biosci. Eng. 10, 445 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of MathematicsSemnan UniversitySemnanIran

Personalised recommendations