An Isolation Model for Tuberculosis Dynamics with Optimal Control Application

Adekunle Oluseye Sangotola; Aanuoluwapo Joshua Adigun; Oluwole Adegoke Nuga; Simeon Adeyemo; Pascal Kingsley Kataboh; Oluwashola Temitayo Akinde; Olawale Sunday Obabiyi

doi:10.5614/cbms.2025.8.1.4

Authors

Adekunle Oluseye Sangotola Department of Physical Sciences, Bells University of Technology, Ota 112104, Nigeria
Aanuoluwapo Joshua Adigun STEM division, Colby Community College, KS 67701, USA
Oluwole Adegoke Nuga Department of Physical Sciences, Bells University of Technology, Ota 112104, Nigeria
Simeon Adeyemo Department of Medicine, University of California, Irvine, Orange, CA 92868, USA
Pascal Kingsley Kataboh Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
Oluwashola Temitayo Akinde Department of Physical Sciences, Bells University of Technology, Ota 112104, Nigeria
Olawale Sunday Obabiyi Department of Mathematics, University of Ibadan, Ibadan 200005, Nigeria

DOI:

https://doi.org/10.5614/cbms.2025.8.1.4

Keywords:

basic reproduction number, equilibrium, lyapunov function, stability, sensitivity analysis

Abstract

Tuberculosis (TB) remains a persistent global health challenge, worsened by asymptomatic carriers who contribute to undetected transmission. An SIQR mathematical model that classifies infected individuals into symptomatic and asymptomatic classes, with isolation as the primary intervention, is formulated in this study. We establish the positivity and invariant region to ensure epidemiological relevance and derive the basic reproduction number, R0, as a threshold for disease persistence. The model analysis reveals that the diseasefree equilibrium is both locally and globally asymptotically stable if R0 < 1, while an endemic equilibrium also exists if R0 > 1. The key parameters influencing transmission dynamics are identified through sensitivity analysis. Furthermore, an optimal control framework is formulated using the Pontryagin?s maximum principle to assess the efficacy of isolation in reducing disease burden while minimizing associated costs. Numerical simulations demonstrate that well-implemented isolation significantly curtails TB spread, highlighting its potential as a targeted intervention.

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