Mathematical Model for the Transmission Dynamics of HIV/Aids and TB Co-Infection

Authors

  • Abdulfatai A. Momoh Department of Mathematics, Modibbo Adama University of Technology, Yola. Adamawa State, Nigeria
  • Abubakar Isah Department of Mathematics, College of Agriculture, Jalingo. Taraba State, Nigeria
  • Nurudeen G. A. Abimbola Department of Mathematics, Federal College of Education (T), Gombe. Gombe State, Nigeria
  • Deborah Mathias Department of Biotechnology, Modibbo Adama University of Technology, Yola. Adamawa State, Nigeria

DOI:

https://doi.org/10.4314/cajost.v1i1.18

Keywords:

Tuberculosis, HIV/AIDS, Co-infection, Basic reproduction number

Abstract

This paper presents a mathematical model for the transmission dynamics of
HIV/AIDS and TB co-infection. The model is governed by seven (7) system of
ordinary differential equations namely: Susceptible, Latent TB, TB infectious,
Treated TB, HIV infected, HIV/AIDS and TB co-infected and AIDS. The disease
free and endemic equilibrium points were obtained for HIV/AIDS sub model, TB
sub model and HIV/AIDS and TB co-infection model. We also derived
reproduction numbers for HIV/AIDS sub model, TB sub model and HIV/AIDS and
TB co-infection model. It was established that the model is locally and globally
asymptotically stable provided that
R0 <1
and unstable when
R0 >1.
Numerical simulation shows that treatment of TB reduces the spread of TB
among TB infected and HIV/TB individuals

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Published

26-02-2019

Issue

Vol. 1 No. 1 (2019): CaJoST

Section

Articles

How to Cite

Mathematical Model for the Transmission Dynamics of HIV/Aids and TB Co-Infection. (2019). CaJoST, 1(1), 71-82. https://doi.org/10.4314/cajost.v1i1.18

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