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.
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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.
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.
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.
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.
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.
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.
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.
Bhunu, C. P., Garira, W., Mukandavire, Z., & Zimba, M. (2008). Tuberculosis transmission model with chemoprophylaxis and treatment. Bull. Math. Biol., 70(4), 1163–1191.
Bhunu, C. P., Garira, W., & Mukandavire, Z. (2009). Modeling HIV/AIDS and Tuberculosis coinfection. Bull. Math. Biol., 71, 1745–1780.
Birkhoff, G. & Rota, G. C. (1982). Ordinary differential equations. Needham Heights: Ginn.
Bothamley, G. H. (2005). Smoking and tuberculosis: a chance or causal association? Thorax, 60, 527–528.
Brown, K. E., & Campbell, A. H. (1961). Tobacco, alcohol and tuberculosis. Br. J. Dis. Chest, 55, 150–158.
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.
Carr, J. (1981). Applications centre manifold theory. New York: Springer.
Castillo-Chavez, C., & Song, B. (2004). Dynamical models of tuberculosis and their applications. Math. Biosci. Eng., 1(2), 361–404.
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.
Chiang, C. (2005). Exogenous reinfection in tuberculosis. Lancet Infect. Dis., 5(10), 629–636.
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.
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.
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.
Dhamgaye, T. M. (2008). Tabacco smoking and pulmonary tuberculosis: a case-control study. J. Indian Med. Assoc., 106, 216–219.
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.
Dye, C., & William, B. G. (2000). Criteria for the control of drug resistant tuberculosis. Proc. Natl. Acad. Sci. USA, 97, 8180–8185.
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.
Edwards, J. H. (1957). Contribution of cigarette smoking to respiratory diseases. Br. J. Prev. Soc. Med., 11, 10.
Feng, Z., Chavez, C. C., & Capurro, A. F. (2000). A model for tuberculosis with exogenous reinfection. Theor. Popul. Biol., 57, 235–247.
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.
Frech, T. F., & Higley, L. H. (1916). The evils of tobacco and cigarettes. Butler: Higley, p. 61.
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.
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.
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.
Greenwood, M. (1977). Epidemics and crowd diseases: an introduction to the study of epidemiology. New York: Arno Press.
Gupta, K. B., & Gupta, R. (2001). Association between smoking and tuberculosis. Ind. J. Tuberc., 50, 5–7.
Gupta, D., Aggarwal, A. M., Kumar, S., & Jindal, S. K. (2001). Smoking increases the risk of pulmonary tuberculosis. J. Environ. Med., 3(1), 65.
Home, H. (1996). Tuberculosis and other mycobacterial diseases. In Cook, G. (Ed.), Manson, S, Tropical diseases (p. 971). London: WB Saunders.
Kellogg, J. H. (1922). Tobaccoism or how tobacco kills (pp. 51–55). Battle Creek: Modern Medicine.
Kiple, K. F. (1993). The Cambridge world history of human disease. Cambridge: Cambridge University Press.
Kolappan, C., & Gopi, P. G. (2002). Tobacco smoking and pulmonary tuberculosis. Thorax, 57, 964–966.
Korobeinikov, A., & Wake, G. C. (2002). Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models. Appl. Math. Lett., 15, 955–960.
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.
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.
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.
Lowe, C. R. (1956). An association between smoking and respiratory diseases. Br. Med. J., 2, 108.
Maher, D., Chaulet, P., Spinaci, S., & Harries, A. (1997). Treatment of tuberculosis: guidelines for national programmes (2nd ed., p. 13). Switzerland: WHO.
Mathers, C. D., & Loncar, D. (2006). Projections of global mortality and burden of disease from 2002 to (2030). PLoS Med., 3(11), e442.
Maurya, V., Vijayan, V. K., & Shah, A. (2002). Smoking and tuberculosis: an association overlooked. Int. J. Tuberc. Lung Dis., 6, 942–951.
McCluskey, C. C. (2006). Lyapunov functions for tuberculosis models with fast and slow progression. Math. Biosci. Eng., 3(4), 603–614.
Milhatan, F., Defta, D., & Tabcu, E. (1995). A profile of the smoker with pulmonary tuberculosis. Pnemotiziologia, 44(12), 33.
MMWR (2003). Cigarette smoking-attributable morbidity—US, 2000. CDC Morb. Mort. Wkly. Rep., 52(35), 842–844.
Nagpaul, D. R. (1996). Editorial. Tobacco use. Ind. J. Tuberc., 43, 1.
Perlman, D. C., Perkins, M. P., Paone, D. et al. (1997). “Shot gunning” as illicit drug smoking practice. Subst. Abuse Treat., 14(1), 3.
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.
Raimundoy, S. M., & Yang, H. M. (2006). Transmission of tuberculosis with exogenous re-infection and endogenous reactivation. Math. Popul. Stud., 13, 181–203.
Rao, K. N. (1996). Diet in tuberculosis. Ind. J. Tuberc., XIII(3), 83–93.
Riley, R. R. (1982). Disease transmission and contagion control. Am. Rev. Respir. Dis., 125(5), 16.
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.
Sharomi, O., & Gumel, A. B. (2008). Curtailing smoking dynamics: a mathematical modeling approach. Appl. Math. Comput., 195(2), 475–499.
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.
Stephenson, J. (2008). TB progress slowing. JAMA, 299(15), 1764.
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.
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.
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.
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.
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.
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.
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.
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.
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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
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DOI: https://doi.org/10.1007/s11538-010-9568-6