Modeling the joint epidemics of TB and HIV in a South African township

  • Nicolas Bacaër
  • Rachid Ouifki
  • Carel Pretorius
  • Robin Wood
  • Brian Williams
Article

DOI: 10.1007/s00285-008-0177-z

Cite this article as:
Bacaër, N., Ouifki, R., Pretorius, C. et al. J. Math. Biol. (2008) 57: 557. doi:10.1007/s00285-008-0177-z

Abstract

We present a simple mathematical model with six compartments for the interaction between HIV and TB epidemics. Using data from a township near Cape Town, South Africa, where the prevalence of HIV is above 20% and where the TB notification rate is close to 2,000 per 100,000 per year, we estimate some of the model parameters and study how various control measures might change the course of these epidemics. Condom promotion, increased TB detection and TB preventive therapy have a clear positive effect. The impact of antiretroviral therapy on the incidence of HIV is unclear and depends on the extent to which it reduces sexual transmission. However, our analysis suggests that it will greatly reduce the TB notification rate.

Keywords

HIV TB Epidemic model Bifurcation diagram 

Mathematics Subject Classification (2000)

34C60 92D30 

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Nicolas Bacaër
    • 1
  • Rachid Ouifki
    • 2
  • Carel Pretorius
    • 2
  • Robin Wood
    • 3
  • Brian Williams
    • 4
  1. 1.Institut de Recherche pour le Développement (IRD)BondyFrance
  2. 2.SACEMA, DST/NRF Centre of Excellence in Epidemiological Modelling and AnalysisStellenbosch UniversityStellenboschSouth Africa
  3. 3.Desmond Tutu HIV Centre, Institute of Infectious Disease and Molecular MedicineUniversity of Cape TownCape TownSouth Africa
  4. 4.Stop TB DepartmentWorld Health OrganizationGenevaSwitzerland