Sensitivity Analysis for High and Low Risk Tuberculosis Model
DOI:
https://doi.org/10.37375/cgkp0642Keywords:
Tuberculosis (TB), Next Generation Matrix, Basic Reproduction NumberR_0, Sensitivity, High risk, Low riskAbstract
This study investigates the sensitivity of parameters related to tuberculosis (TB). A proposed model is formulated based on a system of nonlinear ordinary differential equations, and hence a theoretical analysis of the model is conducted. The model is divided into six compartmental classes: susceptible, vaccinated, population which has high risk to become infection by (TB), population which has low risk to become infection by (TB), infectious, recovery individuals.
The Next Generation Matrix (NGM) method is employed to calculate the basic reproduction number, which appeared as a form in several parameters, a sensitivity analysis is conducted to identify the parameters that significantly influence.
References
Agbata, B. C., Cenaj, E., Agbebaku, D. F., Collins, O. C., Dervishi, R., Emadifar, H., ... & Mbah, G. C. E. (2025). Mathematical Analysis of the Transmission Dynamics of Malaria and Tuberculosis Co‐Infection with Control Strategies. Engineering Reports, 7(6), e70210.
Baqi, A. I. (2025). A fractional order model for the dynamics of tuberculosis spread. Commun. Math. Biol. Neurosci., 2025, Article-ID.
Chasanah, S. L., Aldila, D., & Tasman, H. (2019, March). Mathematical analysis of a tuberculosis transmission model with vaccination in an age structured population. In AIP Conference Proceedings (Vol. 2084, No. 1). AIP Publishing.
DAa, A., AIb, A., ABc, A., & APe, B. (2025). A Review on the Diagnostic Accuracy of Tongue Swab on Tuberculosis (TB) Detection Rates.
Diekmann, O., Heesterbeek, J. A. P. & Metz, J. A. J. 1990. ''On the definition and computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations''. J. Math. Biol. 28, 365 –382.
Diekmann, O., Heesterbeek, J. A. P., & Roberts, M. G. (2010). The construction of next generation matrices for compartmental epidemic models. Journal of the royal society interface.
El-Mesady, A., Peter, O. J., Omame, A., & Oguntolu, F. A. (2024). Mathematical analysis of a novel fractional order vaccination model for Tuberculosis incorporating susceptible class with underlying ailment. International Journal of Modelling and Simulation, 1-25.
Fuller, N. M., McQuaid, C. F., Harker, M. J., Weerasuriya, C. K., McHugh, T. D., & Knight, G. M. (2024). Mathematical models of drug-resistant tuberculosis lack bacterial heterogeneity: A systematic review. PLoS pathogens, 20(4), e1011574
Gebregergs, G. B., Berhe, G., Gebrehiwot, K. G., & Mulugeta, A. (2024). Predicting tuberculosis incidence and its trend in tigray, ethiopia: a reality-counterfactual modeling approach. Infection and Drug Resistance, 3241-3251.
Kozhokaru, A., Ogorodniychuk, I., Yakymets, V., Buyun, L., & Perina, Y. (2025). Epidemiological Monitoring of Tuberculosis among Military Personnel in Ukraine: the Impact of the War and Key Priorities for the Development of the National Tuberculosis Prevention Program. Science and Innovation, 21(3), 99-109.
Liu, S., Lin, T., & Pan, Y. (2025). Vitamin D supplementation for tuberculosis prevention: A meta-analysis. Biomolecules and Biomedicine.
Malek, A., & Hoque, A. (2024). Mathematical model of tuberculosis with seasonality, detection, and treatment. Informatics in Medicine Unlocked, 49, 101536.
Ochieng, F. O. (2024). Mathematical Modeling of Tuberculosis Transmission Dynamics with Reinfection and Optimal Control. Engineering Reports, e13068
OLAOSEBIKAN, M. L., & KOLAWOLE, M. K. (2024). Mathematical Model of Tuberculosis Transmission Dynamics with Vaccination.
Ossaiugbo, M. I., & Okposo, N. I. (2021). Mathematical modeling and analysis of pneumonia infection dynamics. Science world journal, 16(2), 73-80.
Peter, O. J., Abidemi, A., Fatmawati, F., Ojo, M. M., & Oguntolu, F. A. (2024). Optimizing tuberculosis control: a comprehensive simulation of integrated interventions using a mathematical model. Mathematical Modelling and Numerical
Peter, O. J., Aldila, D., Ayoola, T. A., Balogun, G. B., & Oguntolu, F. A. (2025). Modeling tuberculosis dynamics with vaccination and treatment strategies. Scientific African, 28, e02647.
Qureshi, Z. A., Qureshi, S., Shaikh, A. A., & Shahani, M. Y. (2025). Optimizing tuberculosis dynamics through a comparative evaluation of mathematical models. Commun. Math. Biol. Neurosci., 2025, Article-ID.
Rana, P. S., and N. Sharma. "Mathematical modeling and analysis with various parameters, for infection dynamics of Tuberculosis." In Journal of Physics: Conference Series, vol. 1504, no. 1, p. 012007. IOP Publishing, 2020.
Rasheed, S., Iyiola, O. S., Oke, S. I., & Wade, B. A. (2024). Exploring a mathematical model with saturated treatment for the co-dynamics of tuberculosis and diabetes. Mathematics, 12(23), 3765.
Rodrigues, H. S., Monteiro, M. T. T., & Torres, D. F. (2013). Sensitivity analysis in a dengue epidemiological model. In Conference papers in science (Vol. 2013, No. 1, p. 721406). Hindawi Publishing Corporation.
Vaachia, V., & Terna, M. T. (2022). Sensitivity analysis of a tuberculosis (tb) mathematical model. medRxiv, 2022-05.
Yavuz, M., Ozköse, F., Akman, M., & Tastan, Z. T. (2023). A new mathematical model for tuberculosis epidemic under the consciousness effect. Mathematical Modelling and Control, 3(2), 88-103.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Scientific Journal for Faculty of Science-Sirte University

This work is licensed under a Creative Commons Attribution 4.0 International License.







