Threshold Dynamics of an HIV-TB Co-infection Model with Multiple Time Delays


  • M. Pitchaimani Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai- 600 005, Tamil Nadu, India.
  • Saranya Devi A Ramanujan Institute for Advanced study in Mathematics, University of Madras



Bifurcation, Co-infection, Delay Differential equations, HIV- TB, Stability.


In this article, a mathematical model to study the dynamics of
HIV-TB co-infection with two time delays is proposed and analyzed.
We compute the basic reproduction number for each disease (HIV and
TB) which acts as a threshold parameters. The disease dies out when
the basic reproduction number of both diseases are less than unity
and persists when the basic reproduction number of atleast one of the
disease is greater than unity. A numerical study on the model is also
performed to investigate the influence of certain key parameters on the
spread of the disease. Mathematical analysis of our model shows that
switching co-infection (HIV and TB) to single infection (HIV) can be
achieved by imposing treatment for both the disease simultaneously
as TB eradication is made possible with effective treatment.


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How to Cite

Pitchaimani, M., & A, S. D. (2022). Threshold Dynamics of an HIV-TB Co-infection Model with Multiple Time Delays. Tamkang Journal of Mathematics, 53(3), 201–228.