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Modelling and analysis of an alcoholism model with treatment and effect of Twitter

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, People’s Republic of China

Special Issues: Transmission dynamics in infectious diseases

A new alcoholism model with treatment and effect of Twitter is introduced. The stability of all equilibria which is determined by the basic reproductive number R 0 is obtained. The occurrence of backward and forward bifurcation for a certain defined range of R 0 are established by the center manifold theory. Numerical results and sensitivity analysis on several parameters are conducted. Our results show that Twitter may be a good indicator of alcoholism model and affect the emergence and spread of drinking behavior.
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Keywords Twitter; treatment; stability; backward; forward bifurcation

Citation: Hai-Feng Huo, Shuang-Lin Jing, Xun-Yang Wang, Hong Xiang. Modelling and analysis of an alcoholism model with treatment and effect of Twitter. Mathematical Biosciences and Engineering, 2019, 16(5): 3561-3622. doi: 10.3934/mbe.2019179


  • 1. World Health Organization, Global status report on alcohol and health, 2014. Avail- able from: https://www.who.int/substance_abuse/publications/global_alcohol_ report/msb_gsr_2014_1.pdf.
  • 2. Shanghai Institute of Environmental Economics Disaster Prevention Laboratory, China, 2018. Available from: http://www.saes.sh.cn/cn/index.asp.
  • 3. R. Bani, R. Hameed and S. Szymanowski, Influence of environmental factors on college alcohol drinking patterns, Math. Biosci. Eng., 10(2013), 1281–1300.
  • 4. G. Mulone and B. Straughan, Modeling binge drinking, Int. J. Biomath. 5(2012), 57–70.
  • 5. S. Mushayabasa and C. P. Bhunu, Modelling the effects of heavy alcohol consumption on the transmission dynamics of gonorrhea, Nonlinear Dynamics, 66(2011), 695–706.
  • 6. S. Lee, E. Jung and C. Castillo-Chavez, Optimal control intervention strategies in low- and high- risk problem drinking populations, Socio-economic Plan. Sci., 44(2010), 258–265.
  • 7. A. Mubayi, P. Greenwood and C. Castillo-Chavez, The impact of relative residence times on the distribution of heavy drinkers in highly distinct environments, Socio-economic Plan. Sci., 44(2010), 45–56.
  • 8. H. F. Huo, Y. L. Chen and H. Xiang, Stability of a binge drinking model with delay, J. Biol. Dynam., 11(2017), 210–225.
  • 9. H. Xiang, Y. P. Liu and H. F. Huo, Stability of an sairs alcoholism model on scale-free networks, Physica A Statist. Mechan., 473(2017), 276–292.
  • 10. J. Cui, Y. Sun and H. Zhu, The impact of media on the control of infectious diseases, J. Dynam. Differ. Equat., 20(2008), 31–53.
  • 11. K. A. Pawelek, A. Oeldorf-Hirsch and L. Rong, Modeling the impact of twitter on influenza epi- demics, Math. Biosci. Eng. 11(2014), 1337–1356.
  • 12. H. F. Huo and X. M. Zhang, Modeling the Influence of Twitter in Reducing and Increasing the Spread of Influenza Epidemics, SpringerPlus, 5(2016), 88.
  • 13. H. F. Huo and X. M. Zhang, Complex dynamics in an alcoholism model with the impact of twitter, Math. Biosci., 281(2016), 24–35.
  • 14. H. F. Huo, P. Yang and H. Xiang, Stability and bifurcation for an seis epidemic model with the impact of media, Physica A Statist. Mechan. Appl., 490(2018), 702–720.
  • 15. X. Y. Meng and J. G. Wang, Analysis of a delayed diffusive model with Beddington-DeAngelis functional response, Int. J. Biomath., doi:10.1142/S1793524519500475.
  • 16. H. Xiang, M. X. Zou and H. F. Huo, Modeling the Effects of Health Education and Early Ther- apy on Tuberculosis Transmission Dynamics, International Journal of Nonlinear Sciences and Numerical Simulation, DOI:https://doi.org/10.1515/ijnsns-2016-0084.
  • 17. H. Xiang, Y. Y. Wang and H. F. Huo, Analysis of the binge drinking models with demographics and nonlinear infectivity on networks, J. Appl. Anal. Comput. 8(2018), 1535–1554.
  • 18. Y. L. Cai, J. J. Jiao and Z. J. Gui, Environmental variability in a stochastic epidemic model, Appl. Math. Comput., 329(2018), 210–226.
  • 19. Z. Du and Z. Feng, Existence and asymptotic behaviors of traveling waves of a modified vector- disease model, Commu. Pure Appl. Anal., 17(2018), 1899–1920.
  • 20. X. B. Zhang, Q. H. Shi and S. H. Ma, Dynamic behavior of a stochastic SIQS epidemic model with levy jumps, Nonlinear Dynam., 93(2018), 1481–1493.
  • 21. W. M. Wang, Y. l. Cai and Z. Q. Ding, A stochastic differential equation SIS epidemic model incorporating Ornstein-Uhlenbeck process, Physica A Statist. Mechan. Appl., 509(2018), 921– 936.
  • 22. X. Y. Meng and Y. Q. Wu, Bifurcation and control in a singular phytoplankton-zooplankton-fish model with nonlinear fish harvesting and taxation, Int. J. Bifurc. Chaos, 28(2018), 1850042.
  • 23. National Institute on Alcohol Abuse and Alcoholism, United States of America, 2018. Available from: https://www.niaaa.nih.gov/.
  • 24. H. F. Huo, F. F. Cui and H. Xiang, Dynamics of an saits alcoholism model on unweighted and weighted network, Physica A Statist. Mechan., 496(2018), 321–335.
  • 25. H. F. Huo, R. Chen and X. Y. Wang, Modelling and stability of HIV/AIDS epidemic model with treatment, Appl. Math. Modell., 40(2016), 6550–6559.
  • 26. H. F. Huo and M. X. Zou, Modelling effects of treatment at home on tuberculosis transmission dynamics, Appl. Math. Modell., 40(2016), 9474–9484.
  • 27. P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equi- libria for compartmental models of disease transmission, Math. Biosci., 180(2002), 29–48.
  • 28. L. Salle and P. Joseph, The stability of dynamical systems, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1976.
  • 29. C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1(2004), 361–401.
  • 30. A. D. Lê, D. Funk, S. Lo, et al., Operant self-administration of alcohol and nicotine in a preclinical model of co-abuse, Psychopharmacology, 231(2014), 4019–4029.


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