Skip to main content

Advertisement

SpringerLink
Log in

Tuberculosis Transmission Model with Chemoprophylaxis and Treatment

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

Abstract

A tuberculosis model which incorporates treatment of infectives and chemoprophylaxis is presented. The model assumes that latently infected individuals develop active disease as a result of endogenous re-activation, exogenous re-infection and disease relapse, though a small fraction is assumed to develop active disease soon after infection. We start by formulating and analyzing a TB model without any intervention strategy that we extend to incorporate chemoprophylaxis and treatment of infectives. The epidemic thresholds known as reproduction numbers and equilibria for the models are determined, and stabilities analyzed. The reproduction numbers for the models are compared to assess the possible community benefits achieved by treatment of infectives, chemoprophylaxis and a holistic approach of these intervention strategies. The study shows that treatment of infectives is more effective in the first years of implementation (≈ 10 years) as treatment results in clearing active TB immediately and there after chemoprophylaxis will do better in controlling the number of infectives due to reduced progression to active TB.

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

  • Aparicio, J.P., Capurro, A.F., Castillo-Chavez, C., 2000a. Transmission and dynamics of tuberculosis on generalised households. J. Theor. Biol. 206, 327–341.

    Article  Google Scholar 

  • Aparicio, J.P., Capurro, A.F., Castillo-Chavez, C., 2000b. On the fall and rise of tuberculosis. Technical Report Series, BU-1477-M, Department of Biometrics, Cornell University.

  • Aparicio, J.A., Capurro, A.F., Castillo-Chavez, C., 2002. Markers of disease evolution: the case of tuberculosis. J. Theo. Biol. 215, 227–237.

    Article  MathSciNet  Google Scholar 

  • Blower, S.M., Mclean, A.R., Porco, T.C., Small, P.M., Hopewell, P.C., Sanchez, M.A., Moss, A.R., 1995. The intrinsic transmission dynamics of tuberculosis epidemics. Nat. Med. 1(8), 44.

    Article  Google Scholar 

  • Blower, S.M., Small, P.M., Hopewell, P.C., 1996. Control Strategies for tuberculosis epidemics: new models for old problems. Science 273, 497–500.

    Article  Google Scholar 

  • Blower, S.M., Porco, T.C., Lietman, T.M., 1998. Tuberculosis: The evolution of antibiotic resistance and the design of epidemic control strategies. In: Horn, M.A., Simonett, G., Webb, G.F. (Eds.), Mathematical Models in Medical and Health Science. Vanderbilt University Press, Nashville.

    Google Scholar 

  • Castillo-Chavez, C., Feng, Z., 1997. To treat or not to treat: the case of tuberculosis. J. Math. Biol. 35, 629–656.

    Article  MATH  MathSciNet  Google Scholar 

  • Chintu, C., Mwinga, A., 1999. An African perspective of tuberculosis and HIV/AIDS. Lancet 353, 997.

    Article  Google Scholar 

  • Coleman, D.C., Slutkin, G., 1984. Chemoprophylaxis against tuberculosis [Topics in primary care medicine]. West. J. Med. 40(1), 106–110.

    Google Scholar 

  • Davies, P.D.O., 1999. Multi-drug resistant tuberculosis, Priory Lodge Education Ltd.

  • De Cock, K.M., Chaisson, R.E., 1999. Will DOTS do it? A reappraisal of tuberculosis control in countries with high rates of HIV infection. Int. J. Tuberc. Lung Dis. 3, 457–465.

    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 

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

    Article  MATH  Google Scholar 

  • Frieden, T., Driver, R.C., 2003. Tuberculosis control: past 10 years and future progress. Tuberculosis 83, 82–85.

    Article  Google Scholar 

  • Hsu Schmizt, S.F., 2000. Effects of treatment or/and vaccination on HIV transmission in homosexuals with genetic heterogeneity. Math. Biosci. 167, 1–18.

    Article  Google Scholar 

  • Hsu Schmizt, S.F., 2002. Effects of genetic heterogeneity on HIV transmission in homosexuals populations. In: Castillo-Chavez, C., Blower, S., van den Driessche, P., Kirshner, D., Yakubu, A.-A. (Eds.), Mathematical Approaches for Emerging and Re-emerging Infectious Diseases: Models, Methods and Theory, pp. 245–260. Springer, Berlin.

    Google Scholar 

  • Li, M.Y., Muldowney, J.S., 1995. Global stability for the SEIR model in epidemiology. Math. Biosci. 125, 155–164.

    Article  MATH  MathSciNet  Google Scholar 

  • Li, M.Y., Smith, H.L., Wang, L., 1999a. Global dynamics of an SEIR epidemic model. SIAM J. Appl. Math. 62, 58–69.

    MathSciNet  Google Scholar 

  • Li, M.Y., Graef, J.R., Wang, L.C., Karsai, J., 1999b. Global dynamics of an SEIR model with varying total population size. Math. Biosci. 160, 191–213.

    Article  MATH  MathSciNet  Google Scholar 

  • Miller, B., 1993. Preventive therapy for tuberculosis. Med. Clin. North Am. 77, 1263–1275.

    Google Scholar 

  • Muldowney, J.S., 1990. Compound matrices and ordinary differential equations. Rocky Mount. J. Math. 20, 857–871.

    Article  MATH  MathSciNet  Google Scholar 

  • Porco, T.C., Blower, S.M., 1998. Quantifying the intrinsic transmission dynamics of tuberculosis. Theor. Popul. Biol. 54, 117–132.

    Article  MATH  Google Scholar 

  • Raviglione, M.C., 2002. Pio, Evolution of WHO, 1948–2001 policies for tuberculosis control. Lancet 359, 775–780.

    Article  Google Scholar 

  • Raviglione, M.C., Dye, C., Schmizt, S., Kochi, A., 1997. For the global surveillance and monitoring project: assessment of worldwide tuberculosis control. Lancet 350, 624–629.

    Article  Google Scholar 

  • Smith, P.G., Moss, A.R., 1994. Epidemiology of tuberculosis. In: Bloom, B. (Ed.), Tuberculosis Pathogenisis and Control, pp. 47–59. ASM, Washington.

    Google Scholar 

  • Snider, D.E., Raviglione, M., Kochi, A., 1994. Global burden of tuberculosis. In: Bloom, B. (Ed.), Tuberculosis Pathogenisis and Control. ASM, Washington.

    Google Scholar 

  • Song, B., Castillo-Chavez, C., Apariciom, J.P., 2002. Tuberculosis models with fast and slow dynamics: the role of close and casual contacts. Math. Biosci. 180, 187–205.

    Article  MATH  MathSciNet  Google Scholar 

  • Styblo, K., 1991. Epidemiology of Tuberculosis: Selected Papers, Royal Netherlands Tuberculosis Association, The Hague.

  • Thieme, H.R., 1993. Persistence under relaxed point-dissipativity (with applications to an epidemic model). SIAM J. Math. Anal. Appl. 24, 4270–435.

    MathSciNet  Google Scholar 

  • Van den Driesche, P., Watmough, J., 2005. Reproduction numbers and sub-threshold endemic equilibria for the compartmental models of disease transmission. Math. Biosci. 180, 29–48.

    Google Scholar 

  • Vynnycky, E., Fine, P.E.M., 1997. The natural history of tuberculosis: the implications of age dependent risks of disease and the role of reinfection. Epidemiol. Infect. 119, 183–201.

    Article  Google Scholar 

  • Vynnycky, E., Fine, P.E.M., 1998. The long-term dynamics of tuberculosis and other diseases with long serial: the implications of and for changing reproduction numbers. Epidemiol. Infect. 121, 309–324.

    Article  Google Scholar 

  • World Health Organisation, 1999. Preventive therapy against tuberculosis in people living with HIV. Wkly Epidemiol. Rec. 74, 385–398, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    C. P. Bhunu, W. Garira & Z. Mukandavire

  2. Department of Environmental and Health Sciences, National University of Science and Technology, Bulawayo, Zimbabwe

    M. Zimba

Authors
  1. C. P. Bhunu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Garira
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Z. Mukandavire
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Zimba
    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., Garira, W., Mukandavire, Z. et al. Tuberculosis Transmission Model with Chemoprophylaxis and Treatment. Bull. Math. Biol. 70, 1163–1191 (2008). https://doi.org/10.1007/s11538-008-9295-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-008-9295-4

Keywords

Search

Navigation