On the Dynamics of HIV–Tuberculosis Coinfection Model with Temporal Recovery from Tuberculosis: An Analysis

Abstract

The current study is an attempt to frame a deterministic compartmental model for HIV–TB coinfection, considering temporary recovery from Tuberculosis (TB) after treatment (the possibility of reinfection with TB even after recovery). The proposed HIV–TB coinfection model is a composite of an susceptible–infected (SI) type HIV/AIDS model and a susceptible–exposed–infected–recovered type TB model. In the beginning, the HIV–TB model is constructed, followed by the qualitative investigation of the model. The equilibrium points of the model are obtained and have been examined in detail. Further, the basic reproduction number for the HIV–TB coinfection model has been computed, and the proposed model has been simulated numerically to investigate the effect of treatment on HIV–TB coinfection. Analysis of the model claims the existence of interior equilibrium when both HIV and TB reproduction numbers are more than unity. The results exhibit that TB treatment will be the most efficient in discarding the HIV–TB coinfection disease whenever the basic reproduction of HIV–TB is less than one. In addition, our results suggest that the reinfection of TB after recovery impacts HIV–TB transmission. It has been found that reinfection makes disease eradication more challenging. As, in the presence of reinfection, the total infected cases are always higher than the infected cases in the absence of reinfection.