Sensitivity Analysis of a Tuberculosis Transmission Model with Incomplete Treatment

Joko Harianto, Diki Fernandi

Abstract


Tuberculosis (TB) remains a major global health concern due to its complex transmission dynamics and frequent treatment interruptions. This study utilizes a SEITR compartmental model to quantitatively analyze the spread and control of TB. The model calculates the basic reproduction number, disease-free equilibrium, and endemic equilibrium to evaluate system stability. Sensitivity analysis identifies key parameters influencing the infected population: effective contact rate, natural mortality rate, population recruitment rate, and treatment rate. Among these, the effective contact rate and natural mortality rate significantly impact disease persistence. The findings suggest that effective TB control can be achieved through early detection and isolation of infectious individuals, timely and proper treatment, improved indoor ventilation, and the consistent use of masks by active TB patients. This model-based approach offers empirical evidence to inform public health policies, highlighting critical intervention points to interrupt TB transmission and improve treatment outcomes.


Keywords


Basic Reproduction Number; Sensitivity Analisys; Tubercolusis

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References


1] J. Zhang and G. Feng, “Global stability for a tuberculosis model with isolation and incomplete treatment,” Computational and Applied Mathematics, vol. 34, no. 3, pp. 1237–1249, 2015.
[2] A. H. Permatasari and R. H. S. Utomo, “Analysis of tuberculosis dynamical model with different effects of treatment,” Journal of Fundamental Mathematics and Applications, vol. 4, no. 2, pp. 193–202, 2021.
[3] Y. Yang, J. Li, Z. Ma, and L. Liu, “Global stability of two models with incomplete treatment for tuberculosis,” Chaos, Solitons and Fractals, vol. 43, no. 1–12, pp. 79–85, 2010.
[4] A. U. Kalu and S. C. Inyama, “Mathematical model of the role of vaccination and treatment on the transmission dynamics of tuberculosis,” General Mathematics Notes, vol. 11, no. 1, pp. 11–23, 2012.
[5] L. K. Beay and N. Anggriani, “Dynamical analysis of a modified epidemic model with saturated incidence rate and incomplete treatment,” Axioms, vol. 11, no. 6, pp. 1–21, 2022.
[6] L. Wang, “Global dynamical analysis of hiv models with treatments,” International Journal of Bifurcation and Chaos, vol. 22, no. 9, pp. 1–11, 2012.
[7] H. Guo and M. Y. Li, “Global stability of the endemic equilibrium of a tuberculosis model with immigration and treatment,” Canadian Applied Mathematics Quarterly, vol. 19, no. 1, pp. 185–197, 2011.268
[8] X. Zhou, X. Shi, and H. Cheng, “Modelling and stability analysis for a tuberculosis model with healthy education and treatment,” Computational and Applied Mathematics, vol. 32, no. 2, pp. 245–260, 2013.
[9] W. Nur, M. Magfirah, D. Darmawati, and A. Ansar, “Stability analysis of tuberculosis sits model,” Journal of Mathematical Theory and Applications, vol. 2, no. 2, pp. 33–36, 2021.
[10] A. H. Permatasari and R. H. S. Utomo, “Local stability analysis of tuberculosis transmission model with treatment effectiveness,” in AIP Conference Proceedings, vol. 2738, 2023, pp. 1–275
[11] P. Prakitsri, A. Rangsi, C. Nithijirawat, and N. Para, “A mathematical model of tuberculosis transmission in thailand with vaccination and anti-drug treatment,” Journal of AppliedSciences, vol. 18, no. 1, pp. 116–134, 2019.
[12] S. F. Abimbade, S. Olaniyi, O. A. Ajala, and M. O. Ibrahim, “Optimal control analysis of a tuberculosis model with exogenous re-infection and incomplete treatment,” Optimal Control Applications and Methods, vol. 41, no. 6, pp. 2349–2368, 2020.
[13] H. F. Huo and L. X. Feng, “Global stability of an epidemic model with incomplete treatment and vaccination,” Discrete Dynamics in Nature and Society, vol. 2012, pp. 1–15, 2012.
[14] S. M. Garba, M. A. Safi, and S. Usaini, “Mathematical model for assessing the impact of vaccination and treatment on measles transmission dynamics,” Mathematical Methods in the Applied Sciences, vol. 40, no. 18, pp. 6371–6388, 2017.
[15] N. A. Lestari, Sutimin, et al., “Local stability analysis for tuberculosis epidemic model with different infection stages and treatments,” in Journal of Physics: Conference Series, vol. 1943, 2021, pp. 1–8.
[16] I. Ullah, S. Ahmad, Q. Al-Mdallal, Z. A. Khan, H. Khan, and A. Khan, “Stability analysis of a dynamical model of tuberculosis with incomplete treatment,” Advances in Difference Equations, vol. 2020, no. 1, pp. 1–14, 2020.
[17] S. Marino, I. B. Hogue, C. J. Ray, and D. E. Kirschner, “A methodology for performing global uncertainty and sensitivity analysis in systems biology,” Journal of Theoretical Biology, vol. 254, no. 1, pp. 178–196, 2008.
[18] N. R. Chitnis, “Using mathematical models in controlling the spread of malaria,” Unpublished dissertation, Ph.D. dissertation, The University of Arizona, 2005.
[19] S. Dharmaratne, S. Sudaraka, I. Abeyagunawardena, K. Manchanayake, M. Kothalawala, and W. Gunathunga, “Estimation of the basic reproduction number (R0) for the novel coronavirus disease in srilanka,” Virology Journal, vol. 17, no. 1, pp. 144–156, 2020.
[20] P. Van den Driessche, “Reproduction numbers of infectious disease models,” Infectious Disease Modelling, vol. 2, no. 3, pp. 288–303, 2017.
[21] K. J. B. Villasin and A. R. E. M. R. Lao, “A dynamical analysis of tuberculosis in the philippines,” Philippine Science Letters, vol. 10, no. 1, pp. 29–37, 2017.
[22] Q. Li and F. Wang, “An epidemiological model for tuberculosis considering environmental transmission and reinfection,” Mathematics, vol. 11, no. 11, pp. 1–17, 2023.
[23] World Health Organization, Global Tuberculosis Report 2023, 1st. Geneva: WHO Press.




DOI: https://doi.org/10.18860/cauchy.v11i1.36325

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