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Optimal Control Analysis of HIV-TB Co-infection Model

In: Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment

Author

Listed:
  • Tanvi

    (University of Delhi, Department of Mathematics)

  • Rajiv Aggarwal

    (University of Delhi, Deshbandhu College)

Abstract

In this paper, an HIV/AIDS and TB co-infection model is explored which incorporates detection and treatment for both the diseases. We begin with presenting a co-infection model and then start analyzing the model. The basic reproduction number corresponding to the full model is computed. The disease-free equilibrium point for the model is found to be locally asymptotically stable when its corresponding reproduction number is less than unity. The endemic equilibrium points corresponding to HIV and TB exist when their corresponding reproduction number is greater than one. With the aim of minimizing infectives and the cost of applying efforts towards the detection and treatment, optimal control analysis is performed for the full model using Pontryagin’s maximum principle. Numerical simulations emphasize the fact that to reduce co-infection from the population, programs to accelerate the detection of both the diseases are also required along with the treatment.

Suggested Citation

  • Tanvi & Rajiv Aggarwal, 2020. "Optimal Control Analysis of HIV-TB Co-infection Model," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment, pages 259-273, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-46306-9_17
    DOI: 10.1007/978-3-030-46306-9_17
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