Skip to main content

Advertisement

SpringerLink
Log in

A Theoretical Assessment of the Effects of Smoking on the Transmission Dynamics of Tuberculosis

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

Smoking has long being associated with tuberculosis. We present a tuberculosis dynamics model taking into account the fact that some people in the population are smoking in order to assess the effects of smoking on tuberculosis transmission. The epidemic thresholds known as the reproduction numbers and equilibria for the model are determined and stabilities analyzed. Qualitative analysis of the model including positivity and persistence of solutions are presented. The model is numerically analyzed to assess the effects of smoking on the transmission dynamics of tuberculosis. Numerical simulations of the model show that smoking enhances tuberculosis transmission, progression to active disease and in a population of smokers, tuberculosis cannot be controlled even when treatment success is assumed to be as high as 88%. Further, analysis of the reproduction numbers indicates that the number of active tuberculosis cases increases as the number of smokers increase.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alcaide, J., Altlet, M. N., & Plans, P. (1996). Cigarette smoking as a risk factor for tuberculosis in young adults: a case-control study. Tuberc. Lung Dis., 77(2), 112.

    Article  Google Scholar 

  • Adelstein, A. M., & Rimingston, J. (1967). Smoking and pulmonary tuberculosis: an analysis based on a study of volunteers for mass miniature radiography. Tubercle, 48, 219–226.

    Article  Google Scholar 

  • Baker, M., Das, D., Venugopal, K., & Howden-Chapman, P. (2008). Tuberculosis associated with household crowding in a developed country. J. Epidemiol. Community Health, 62, 715–721.

    Article  Google Scholar 

  • Bao, Q.-S., Du, Y.-H., & Lu, C.-Y. (2007). Treatment outcome of new pulmonary tuberculosis in Guangzhou, China 1993–2002: a register-based cohort study. BMC Public Health, 7, 344.

    Article  Google Scholar 

  • Bates, M. N., Khalakdina, A., Pai, M., Chang, L., Lessa, F., & Smith, K. R. (2007). Risk of tuberculosis from exposure to tobacco smoke: a systematic review and meta-analysis. Arch. Intern. Med., 167(4), 335–342.

    Article  Google Scholar 

  • Batista, J., d’Arc, L., Albuquerque, M. F. P. M., Ximenes, R. A. A., & Rodrigues, L. C. (2008). Smoking increases the risk of relapse after successful tuberculosis treatment. Int. J. Epidemiol., 37, 841–851.

    Google Scholar 

  • Beaglehole, R., & Yach, D. (2003). Globalisation and the prevention and control of non-communicable disease: the neglected chronic diseases of adults. Lancet, 362(9387), 903–908.

    Article  Google Scholar 

  • Bhunu, C. P., Garira, W., Mukandavire, Z., & Zimba, M. (2008). Tuberculosis transmission model with chemoprophylaxis and treatment. Bull. Math. Biol., 70(4), 1163–1191.

    Article  MathSciNet  MATH  Google Scholar 

  • Bhunu, C. P., Garira, W., & Mukandavire, Z. (2009). Modeling HIV/AIDS and Tuberculosis coinfection. Bull. Math. Biol., 71, 1745–1780.

    Article  MathSciNet  MATH  Google Scholar 

  • Birkhoff, G. & Rota, G. C. (1982). Ordinary differential equations. Needham Heights: Ginn.

    Google Scholar 

  • Bothamley, G. H. (2005). Smoking and tuberculosis: a chance or causal association? Thorax, 60, 527–528.

    Article  Google Scholar 

  • Brown, K. E., & Campbell, A. H. (1961). Tobacco, alcohol and tuberculosis. Br. J. Dis. Chest, 55, 150–158.

    Article  Google Scholar 

  • Caminero, J. A., Pena, M. J., Campos-Herrero, M. I., Rodriguez, J. C., Afonso, O., Martin, C., Pavon, J. M., Torres, M. J., Burgos, M., Cabrera, P., Small, P. M., & Enarson, D. A. (2001). Exogenous reinfection with tuberculosis on a European island with a moderate incidence of disease. Am. J. Respir. Crit. Care Med., 163(3), 717–720.

    Google Scholar 

  • Carr, J. (1981). Applications centre manifold theory. New York: Springer.

    MATH  Google Scholar 

  • Castillo-Chavez, C., & Song, B. (2004). Dynamical models of tuberculosis and their applications. Math. Biosci. Eng., 1(2), 361–404.

    MathSciNet  MATH  Google Scholar 

  • Castillo-Chavez, C., Feng, Z., & Huang, W. (2002). On the computation of R0 and its role on global stability. math.la.asu.edu/chavez/2002/JB276.pdf

  • Chadwick, E. (1842). Report from the Poorl law commissioners on an inquiry into the sanitary conditions of the laboring population of Great Britain. London: HMSO.

    Google Scholar 

  • Chiang, C. (2005). Exogenous reinfection in tuberculosis. Lancet Infect. Dis., 5(10), 629–636.

    Article  MathSciNet  Google Scholar 

  • Cohen, T., Colijn, C., Finklea, B., & Murray, M. (2007). Exogenous re-infection and the dynamics of tuberculosis epidemics: local effects in a network model of transmission. J. R. Soc. Interface, 4, 523–531.

    Article  Google Scholar 

  • Davies, P. D., Yew, W. W., Ganguly, D., Davidow, A. L., Reichman, L. B., Dheda, K., & Rook, G. A. (2006). Smoking and tuberculosis: the epidemiological association and immunopathogenesis. Trans. R. Soc. Trop. Med. Hyg., 100(4), 291–298.

    Article  Google Scholar 

  • den Boon, S., van Lill, S. W. P., Borgdorff, M. W., Verver, S., Bateman, E. D., Lombard, C. J., Enarson, D. A., & Beyers, N. (2005). Association between smoking and tuberculosis infection: a population survey in a high tuberculosis incidence area. Thorax, 60, 555–557.

    Article  Google Scholar 

  • Dhamgaye, T. M. (2008). Tabacco smoking and pulmonary tuberculosis: a case-control study. J. Indian Med. Assoc., 106, 216–219.

    Google Scholar 

  • Diekmann, O., Heesterbeek, J. A. P., & Metz, J. A. P. (1990). On the definition and computation of the basic reproduction ratio \(\mathcal{R}_{0}\) in the model of infectious disease in heterogeneous populations. J. Math. Biol., 2(1), 265–382.

    MathSciNet  Google Scholar 

  • Dye, C., & William, B. G. (2000). Criteria for the control of drug resistant tuberculosis. Proc. Natl. Acad. Sci. USA, 97, 8180–8185.

    Article  Google Scholar 

  • Dye, C., Schele, S., Dolin, P., Pathania, V., & Raviglione, M. (1999). For the WHO global surveillance and monitoring project. Global burden of tuberculosis estimated incidence, prevalence and mortality by country. JAMA, 282, 677–686.

    Article  Google Scholar 

  • Edwards, J. H. (1957). Contribution of cigarette smoking to respiratory diseases. Br. J. Prev. Soc. Med., 11, 10.

    Google Scholar 

  • Feng, Z., Chavez, C. C., & Capurro, A. F. (2000). A model for tuberculosis with exogenous reinfection. Theor. Popul. Biol., 57, 235–247.

    Article  MATH  Google Scholar 

  • Fiore, M. C., Novotny, T., Pierce, J. P., Giovino, G. A., Hatziandreu, E. J., Newcomb, P. A., Surawicz, T. S., & Davis, R. M. (1990). Methods used to quit smoking in the United States. Do cessation programs help? JAMA, 263, 2760–2765.

    Article  Google Scholar 

  • Frech, T. F., & Higley, L. H. (1916). The evils of tobacco and cigarettes. Butler: Higley, p. 61.

    Google Scholar 

  • Frosch, Z. A. K., Dierker, L. C., Rose, J. S., & Waldinger, R. J. (2009). Smoking trajectories, health, and mortality across the adult lifespan. Addict. Behav., 34, 701–704.

    Article  Google Scholar 

  • Gilpin, E. A., Pierce, J. P., & Farkas, A. J. (1997). Duration of smoking abstinence and success in quitting. J. Nat. Cancer Inst., 89, 572–576.

    Article  Google Scholar 

  • Gomes, M. G. M., Franco, A. O., Gomes, M. C., & Medley, G. F. (2004). The reinfection threshold promotes variability in tuberculosis epidemiology and vaccine efficacy. Proc. Biol. Sci., 271(1539), 617–623.

    Article  Google Scholar 

  • Greenwood, M. (1977). Epidemics and crowd diseases: an introduction to the study of epidemiology. New York: Arno Press.

    Google Scholar 

  • Gupta, K. B., & Gupta, R. (2001). Association between smoking and tuberculosis. Ind. J. Tuberc., 50, 5–7.

    Google Scholar 

  • Gupta, D., Aggarwal, A. M., Kumar, S., & Jindal, S. K. (2001). Smoking increases the risk of pulmonary tuberculosis. J. Environ. Med., 3(1), 65.

    Google Scholar 

  • Home, H. (1996). Tuberculosis and other mycobacterial diseases. In Cook, G. (Ed.), Manson, S, Tropical diseases (p. 971). London: WB Saunders.

    Google Scholar 

  • Kellogg, J. H. (1922). Tobaccoism or how tobacco kills (pp. 51–55). Battle Creek: Modern Medicine.

    Google Scholar 

  • Kiple, K. F. (1993). The Cambridge world history of human disease. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Kolappan, C., & Gopi, P. G. (2002). Tobacco smoking and pulmonary tuberculosis. Thorax, 57, 964–966.

    Article  Google Scholar 

  • Korobeinikov, A., & Wake, G. C. (2002). Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models. Appl. Math. Lett., 15, 955–960.

    Article  MathSciNet  MATH  Google Scholar 

  • Korobeineikov, A., & Maini, P. K. (2004). A Lyapunov functional and global properties for SIR and SEIR epidemiological models with nonlinear incidence. Math. Biosci. Eng., 1(1), 57–60.

    MathSciNet  Google Scholar 

  • Lavigne, M., Rocher, I., Steensma, C., & Brassard, P. (2006). The impact of smoking on adherence to treatment for latent tuberculosis infection. BMC Public Health, 6(66).

  • Leistikow, B. N. (2000). The human and financial costs of smoking. Clin. Chest Med., 21(1), 189–197.

    Article  Google Scholar 

  • Lin, H. H., Ezzati, M., & Murray, M. (2007). Tobacco smoke, indoor air pollution and tuberculosis: a systematic review and meta-analysis. PLoS Med., 4(1), e20.

    Article  Google Scholar 

  • Lowe, C. R. (1956). An association between smoking and respiratory diseases. Br. Med. J., 2, 108.

    Article  Google Scholar 

  • Maher, D., Chaulet, P., Spinaci, S., & Harries, A. (1997). Treatment of tuberculosis: guidelines for national programmes (2nd ed., p. 13). Switzerland: WHO.

    Google Scholar 

  • Mathers, C. D., & Loncar, D. (2006). Projections of global mortality and burden of disease from 2002 to (2030). PLoS Med., 3(11), e442.

    Article  Google Scholar 

  • Maurya, V., Vijayan, V. K., & Shah, A. (2002). Smoking and tuberculosis: an association overlooked. Int. J. Tuberc. Lung Dis., 6, 942–951.

    Google Scholar 

  • McCluskey, C. C. (2006). Lyapunov functions for tuberculosis models with fast and slow progression. Math. Biosci. Eng., 3(4), 603–614.

    MathSciNet  MATH  Google Scholar 

  • Milhatan, F., Defta, D., & Tabcu, E. (1995). A profile of the smoker with pulmonary tuberculosis. Pnemotiziologia, 44(12), 33.

    Google Scholar 

  • MMWR (2003). Cigarette smoking-attributable morbidity—US, 2000. CDC Morb. Mort. Wkly. Rep., 52(35), 842–844.

    Google Scholar 

  • Nagpaul, D. R. (1996). Editorial. Tobacco use. Ind. J. Tuberc., 43, 1.

    Google Scholar 

  • Perlman, D. C., Perkins, M. P., Paone, D. et al. (1997). “Shot gunning” as illicit drug smoking practice. Subst. Abuse Treat., 14(1), 3.

    Article  Google Scholar 

  • Pisinger, C., Glümer, C., Toft, U., von Huth, Smith L., Aadahl, M., Borch-Johnsen, K., & Jorgensen, T. (2008). High risk strategy in smoking cessation is feasible on a population-based level. The Inter99 study. Prev. Med., 46, 579–584.

    Article  Google Scholar 

  • Raimundoy, S. M., & Yang, H. M. (2006). Transmission of tuberculosis with exogenous re-infection and endogenous reactivation. Math. Popul. Stud., 13, 181–203.

    Article  MathSciNet  Google Scholar 

  • Rao, K. N. (1996). Diet in tuberculosis. Ind. J. Tuberc., XIII(3), 83–93.

    Google Scholar 

  • Riley, R. R. (1982). Disease transmission and contagion control. Am. Rev. Respir. Dis., 125(5), 16.

    Google Scholar 

  • Shafer, R. W., Singh, S. P., Larkin, C., & Small, P. M. (1995). Exogenous reinfection with multidrug-resistant Mycobacterium tuberculosis in an immunocompetent patient. Tuberc. Lung Dis., 76, 575–577.

    Article  Google Scholar 

  • Sharomi, O., & Gumel, A. B. (2008). Curtailing smoking dynamics: a mathematical modeling approach. Appl. Math. Comput., 195(2), 475–499.

    Article  MathSciNet  MATH  Google Scholar 

  • Sharomi, O., Podder, C. N., Gumel, A. B., & Song, B. (2008). Mathematical analysis of the transmission dynamics of HIV/TB co-infection in the presence of treatment. Math. Biosci. Eng., 5(1), 145–174.

    MathSciNet  MATH  Google Scholar 

  • Stephenson, J. (2008). TB progress slowing. JAMA, 299(15), 1764.

    Google Scholar 

  • Steven, J., & David, M. D. (1998). Cigarette smoking and disease. In: Fishman, A. P., Elias, J. A., Grippi, M. A., Kaiser, L. V., Senior, R. M. (Eds.), Fishman’s pulmonary diseases and disorders, (3rd ed.) (p. 687). New York: McGraw Hill.

    Google Scholar 

  • van den Brande, P., Vanhoenacker, F., & Demedts, M. (2003). Tuberculosis at the beginning of the third millennium: one disease, three epidemics. Eur. Radiol., 13(8), 1767–1770.

    Article  Google Scholar 

  • van den Driesche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for the compartmental models of disease transmission. Math. Biosci., 180, 29–48.

    Article  MathSciNet  Google Scholar 

  • van Rie, A., Warren, R., Richardson, M., Victor, T. C., Gie, R. P., Enarson, D. A., Beyers, N., & van Helden, P. D. (1999). Exogenous reinfection as a cause of recurrent tuberculosis after curative treatment. New Engl. J. Med., 341, 1174–1179.

    Article  Google Scholar 

  • WHO (2000). Press releases. Fact sheet 104. Revised.

  • WHO (2005). Global tuberculosis control: surveillance, planning, and financing. Geneva: World Health Organization, Publication WHO/HTM/TB2005.349.

    Google Scholar 

  • Woo, J., Chan, H. S., Hazlet, C. B., Chau, R., Sham, A., & Davies, P. D. (1996). Tuberculosis among elderly Chinese in residential homes: tuberculin reactivity and estimated prevalence. Gerontology, 42(3), 155.

    Article  Google Scholar 

  • Wu, P., Wilson, K., Dimoulas, P., & Mills, E. J. (2006). Effectiveness of smoking cessation therapies: a systematic review and meta-analysis. BMC Public Health, 6, 300. doi:10.1186/1471-2458-6-300.

    Article  Google Scholar 

  • Yu, G. P., Hsieh, C. C., & Peng, J. (1988). Risk factors associated with the prevalence of pulmonary tuberculosis among sanitary workers in Shanghai. Tubercle, 69, 105–112.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Modelling Biomedical Systems Research Group, National University of Science and Technology, P.O. Box 939, Ascot, Bulawayo, Zimbabwe

    C. P. Bhunu & S. Mushayabasa

  2. Department of Mathematics and Statistics, University of Guelph, Guelph, ON, N1G 2W1, Canada

    J. M. Tchuenche

  3. Department of Veterinary Medicine, University of Cambridge, Cambridge, CB3 OES, UK

    C. P. Bhunu

Authors
  1. C. P. Bhunu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Mushayabasa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. M. Tchuenche
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. P. Bhunu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bhunu, C.P., Mushayabasa, S. & Tchuenche, J.M. A Theoretical Assessment of the Effects of Smoking on the Transmission Dynamics of Tuberculosis. Bull Math Biol 73, 1333–1357 (2011). https://doi.org/10.1007/s11538-010-9568-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-010-9568-6

Keywords

Search

Navigation