Journal of Biological Physics

, Volume 40, Issue 2, pp 139–166

# The role of screening and treatment in the transmission dynamics of HIV/AIDS and tuberculosis co-infection: a mathematical study

Original Paper

## Abstract

In this paper, we present a deterministic non-linear mathematical model for the transmission dynamics of HIV and TB co-infection and analyze it in the presence of screening and treatment. The equilibria of the model are computed and stability of these equilibria is discussed. The basic reproduction numbers corresponding to both HIV and TB are found and we show that the disease-free equilibrium is stable only when the basic reproduction numbers for both the diseases are less than one. When both the reproduction numbers are greater than one, the co-infection equilibrium point may exist. The co-infection equilibrium is found to be locally stable whenever it exists. The TB-only and HIV-only equilibria are locally asymptotically stable under some restriction on parameters. We present numerical simulation results to support the analytical findings. We observe that screening with proper counseling of HIV infectives results in a significant reduction of the number of individuals progressing to HIV. Additionally, the screening of TB reduces the infection prevalence of TB disease. The results reported in this paper clearly indicate that proper screening and counseling can check the spread of HIV and TB diseases and effective control strategies can be formulated around ‘screening with proper counseling’.

### Keywords

Co-infection Basic reproduction number Simulation

## Notes

### Acknowledgments

The authors thank the handling editor and anonymous referees for their valuable comments and suggestions that led to an improvement of our original manuscript. This research was partially supported by the research grants of DST, Govt. of India, via a sponsored research project: SR/S4/MS:681/10.

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