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

In this article, a mathematical model to study the dynamics of HIV-TB coinfection 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.