A tuberculosis model with three infected classes


  • A. O. Sangotola Department of Physical Sciences, Bells University of Technology, Ota, Nigeria
  • S. B. Adeyemo Department of Mathematics and Statistics, California State University, Long Beach, California, USA
  • O. A. Nuga Department of Physical Sciences, Bells University of Technology, Ota, Ogun State, Nigeria
  • A. E. Adeniji Department of Physical Sciences, Bells University of Technology, Ota, Ogun State, Nigeria
  • A. J. Adigun Department of Mathematical Sciences, University of Delaware, U.S.A


Optimal Control, Lyapunov function, Equilibrium, Basic , Jacobian


The dynamics of tuberculosis within a population cannot be adequately represented by a single infectious class. Therefore, this study develops a compartmental model encompassing latent, active, and drug-resistant populations to better capture tuberculosis dynamics in a community. Model analysis reveals that the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number is below one. Moreover, the use of a suitable Lyapunov function demonstrates global asymptotic stability of the disease-free equilibrium point. An endemic equilibrium emerges when the basic reproduction number exceeds one. Sensitivity analysis is conducted for each parameter associated with the basic reproduction number, and optimal control analysis is employed to assess the impact of various control strategies on disease containment. Numerical simulations are conducted to supplement theoretical findings, illustrating the practical implications of the proposed control strategies.


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How to Cite

A tuberculosis model with three infected classes. (2024). Journal of the Nigerian Society of Physical Sciences, 6(1), 1881. https://doi.org/10.46481/jnsps.2024.1881



Mathematics & Statistics

How to Cite

A tuberculosis model with three infected classes. (2024). Journal of the Nigerian Society of Physical Sciences, 6(1), 1881. https://doi.org/10.46481/jnsps.2024.1881