Journal of Mathematical Modelling and Algorithms

, Volume 11, Issue 4, pp 387–408 | Cite as

A Theoretical Analysis of Smoking and Alcoholism

  • C. P. BhunuEmail author
  • S. Mushayabasa


A mathematical model for the spread of alcoholism and smoking is designed and analysed to gain insights into this growing health and social problem. The reproduction number and equilibria states of the model are determined and their local asymptotic stabilities investigated. Analysis of the reproduction number have shown conditions under which encouraging and supporting moderate alcohol drinkers (smokers) to quit alcohol consumption (smoking) is more effective in the control of alcoholism (smoking) than supporting and encouraging alcoholics (smoking addicts) to quit and vice-versa. Numerical simulations show that smoking greatly enhances alcoholism and vice-versa. Thus, as shown by the numerics encouraging and supporting all smokers (alcohol drinkers) to quit smoking (alcohol drinking) also contribute meaningfully to alcohol (smoking) control programmes.


Alcohol drinkers and smokers Mathematical model Reproduction number 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Benedict, B.: Modeling alcoholism as a contagious disease: how infected buddies spread problem drinking. SIAM News 40(3) (2007)Google Scholar
  2. 2.
    Bhunu, C.P., Mushayabasa, S., Tchuenche, M.:. Assessing the effects of smoking on the transmission dynamics of Tuberculosis. Bull. Math. Biol. 73(6), 1333–1357 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bhunu, C.P.: Mathematical analysis of alcoholism. WJMS 8(2), 124–134 (2012)Google Scholar
  4. 4.
    Bhunu, C.P., Mushayabasa, S.: Prostitution and drug (alcohol) misuse: the menacing combination. J. Biol. Syst. 20(2), 177–193 (2012). doi: 10.1142/S0218339012500052 MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bobo, J.K., Husten, C.: Sociocultural influences on smoking and drinking. Alcohol Res. Health 24(4), 231–232 (2000)Google Scholar
  6. 6.
    Botvin, G.J., Malgady, R.G., Griffin, K.W., Scheier, L.M., Epstein, J.A.: Alcohol and marijuana use among rural youth: Interaction of social and intrapersonal influences. Addict. Behav. 23(3), 379–387 (1998)CrossRefGoogle Scholar
  7. 7.
    Brook, J.S., Whiteman, M., Gordon, A.S., Nomura, C., Brook, D.W.: Onset of adolescent drinking: A longitudinal study of intrapersonal antecedents. Adv. Alcohol Subst. Abuse 5(3), 91–110 (1986)CrossRefGoogle Scholar
  8. 8.
    Carr, J: Applications Centre Manifold Theory. Springer, New York (1981)CrossRefzbMATHGoogle Scholar
  9. 9.
    Castillo-Chavez, C., Song, B.: Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 1(2), 361–404 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Conrad, K.M., Flay, B.R., Hill, D.: Why children start smoking cigarettes: predictors of onset. Br. J. Addict. 87(12), 1711–1724 (1992)CrossRefGoogle Scholar
  11. 11.
    Ezzati, M., Lopez, A.D., Rodgers, A., Murray, C.J.L.: Comparative risk assessment group. Selected major risk factors and global and regional burden of disease. Lancet 360, 1347–1360 (2002)CrossRefGoogle Scholar
  12. 12.
    Flay, B.R., Hu, F.B., Flaya, B.R., Phil, D., Richardson, J.: Psychosocial predictors of different stages of cigarette smoking among high school students. Prev. Med. 27, A9–A18 (1998)CrossRefGoogle Scholar
  13. 13.
    Gritz, E.R., Prokhorov, A.V., Hudmon, K.S., Chamberlain, R.M., Taylor, W.C., DiClemente, C.C., Johnston, D.A., Hu, S., Jones, L.A., Jones, M.M., Rosenblum, C.K., Ayars, C.L., Amos, C.I.: Cigarette smoking in a multiethnic population of youth: methods and baseline findings. Prev. Med. 27(3), 365–384 (1998)CrossRefGoogle Scholar
  14. 14.
    Gulliver, S.B., Kamholz, B.W., Helstrom, A.W.: Smoking cessation and alcohol abstinence: what do the data tell us. Alcohol Res. Health 29(3), 208–212 (2006)Google Scholar
  15. 15.
    Hill, A.L., Rand, D.G., Nowak, M.A., Christakis, N.A.: Infectious disease modelling of social contagion in networks. PLOS Comput. Biol. 6(11) (2010)Google Scholar
  16. 16.
    Hughes, J.R.: Combining behavioural therapy and pharmacotherapy for smoking cessation: an update. NIDA Res. Mononogr. 150, 92–109 (1995)Google Scholar
  17. 17.
    Hughes, J.R.: Treating smokers with current or past alcohol dependence. Am. J. Health Behav. 20, 286–290 (1996)Google Scholar
  18. 18.
    Hughes, J.R., Ross, G.L., Callas, P.W.: Nicotine is more reinforcing in smokers with a past history of alcoholism than in smokers without this history. ACER 24(10), 1633–1638 (2000)Google Scholar
  19. 19.
    Mittelmark, M.B., Murray, D.M., Luepker, R.V., Pechacek, T.R., Plate, P.L., Pallonen, U.E.: Predicting experimentation with cigarettes: the childhood antecedents of smoking study (CASS). Am. J. Public Health 77(2), 206–208 (1987)CrossRefGoogle Scholar
  20. 20.
    Mokdad, H.A., Marks, S.J., Stroup, D.F., Gerberding, J.L.: Actual causes of death in the United States of America, 2000. J. Am. Med. Assoc. 291(10), 1238–1245 (2004)CrossRefGoogle Scholar
  21. 21.
    Qiu, Z., Yu, J., Zou, Y.: The asymptotic behavior of a chemostat model. Disc. Cont. Dynam. Syst. - Ser. B4(3), 721–727 (2004)MathSciNetGoogle Scholar
  22. 22.
    Room, R.: Smoking and drinking as complementary behaviours. Biomed. Pharmacother. 58, 111–115 (2004)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Scaffa, M.E.:. Adolescents and alcohol use. In: Henderson, A., Champlin, S., Evashwick, W. (eds.) Promoting Teen Health: Linking Schools, Health Organizations and Community, pp. 78–99. SAGE, Thousand Oaks (1998)Google Scholar
  24. 24.
    Sharomi, O., Gumel, A.B.: Curtailing smoking dynamics: a mathematical modeling approach. Appl. Math. Comput. 195(2), 475–499 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Shiffman, S., Balabanis, M.: Association between alcohol and tobacco. In: Ferting, J.B., Allen, J.P. (eds.) Alcohol and Tobacco: From Basic Science to Clinical Practice (NIH Publication 95-397), pp. 17–37. United States Department of Health and Human Services, Washington, D.C. (1995)Google Scholar
  26. 26.
    Unger, J.B., Chen, X.: The role of social networks and media receptivity in predicting age of smoking initiation: a proportional hazards model of risk and protective factors. Addict. Behav. 24(3), 371–381 (1999)CrossRefGoogle Scholar
  27. 27.
    van den Driesche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for the compartmental models of disease transmission. Math. Biosci. 180, 29–48 (2002)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Walsh, R.A., Bowman, J.A., Tzelepis, F., Lecathelinais, C.: Smoking cessation interventions in Australian drug treatment agencies: a national survey of attitudes and practices. Drug Alcohol Rev. 24, 235–244 (2005)CrossRefGoogle Scholar
  29. 29.
    Wills, T.A., Shiffman, S.: Coping behavior and its relation to substance use: a conceptual framework. In: Shiffman, S., Wills, T.A. (eds.) Coping and Substance Use, pp. 3–24. Academic Press, New York (1985)Google Scholar
  30. 30.
    World Health Organization: Global Status Report on Alcohol. World Health Organization, Geneva (2004)Google Scholar
  31. 31.
    Zullino, D.F., Besson, J., Favrat, B., Krenz, S., Zimmermann, G., Schnyder, C., Borgeat, F.: Acceptance of an intended smoking ban on an alcohol dependence clinic. Eur. Psychiatr. 18, 255–257 (2003)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ZimbabweHarareZimbabwe

Personalised recommendations