Evaluating the impact of vaccination and progression delays on tuberculosis dynamics with disability outcomes: A case study in Saudi Arabia

Kamel Guedri; Rahat Zarin; Mowffaq Oreijah; Kamel Guedri; Rahat Zarin; Mowffaq Oreijah

doi:10.3934/math.2025366

AIMS Mathematics

2025, Volume 10, Issue 4: 7970-8001. doi: 10.3934/math.2025366

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Research article Special Issues

Evaluating the impact of vaccination and progression delays on tuberculosis dynamics with disability outcomes: A case study in Saudi Arabia

1.
Mechanical Engineering Department, College of Engineering and Architecture, Umm Al-Qura University, P.O. Box 5555, Makkah 21955, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), Bangkok 10140, Thailand
3.
King Salman Center for Disability Research, Riyadh 11614, Saudi Arabia

Received: 11 February 2025 Revised: 28 March 2025 Accepted: 31 March 2025 Published: 07 April 2025
MSC : 92D30, 34K13, 65L06

Tuberculosis (TB) remains a major global health concern due to its infectious nature and complex treatment process. In this study, we developed a mathematical model incorporating TB progression, vaccination, latency delays, and disability outcomes. The compartmental model includes seven stages: Susceptible, vaccinated, latent, infectious, quarantined, recovered, and disabled, with time-delay terms capturing disease progression dynamics. The stability analysis of the equilibria was performed, and the sensitivity analysis was conducted using the direct differentiation method. The basic reproduction number $ R_0 $ was derived to assess TB spread under different interventions. Model parameters were estimated using Ordinary Least Squares (OLS) based on Saudi Arabia's TB data (2000–2023). Numerical simulations, solved via the Adams-Bashforth-Moulton method, highlight the impact of delayed latency and quarantine on TB control, emphasizing the need for timely interventions.
- sensitivity analysis,
- disability,
- latency delays,
- modeling,
- vaccination,
- numerical simulations
Citation: Kamel Guedri, Rahat Zarin, Mowffaq Oreijah. Evaluating the impact of vaccination and progression delays on tuberculosis dynamics with disability outcomes: A case study in Saudi Arabia[J]. AIMS Mathematics, 2025, 10(4): 7970-8001. doi: 10.3934/math.2025366

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Abstract

Tuberculosis (TB) remains a major global health concern due to its infectious nature and complex treatment process. In this study, we developed a mathematical model incorporating TB progression, vaccination, latency delays, and disability outcomes. The compartmental model includes seven stages: Susceptible, vaccinated, latent, infectious, quarantined, recovered, and disabled, with time-delay terms capturing disease progression dynamics. The stability analysis of the equilibria was performed, and the sensitivity analysis was conducted using the direct differentiation method. The basic reproduction number $ R_0 $ was derived to assess TB spread under different interventions. Model parameters were estimated using Ordinary Least Squares (OLS) based on Saudi Arabia's TB data (2000–2023). Numerical simulations, solved via the Adams-Bashforth-Moulton method, highlight the impact of delayed latency and quarantine on TB control, emphasizing the need for timely interventions.

References

[1]	Global Tuberculosis Report 2022, World Health Organization, 2022. Available from: https://www.who.int/teams/global-tuberculosis-programme/tb-reports
[2]	Updated TB Treatment Guidelines, World Health Organization, 2023. Available from: https://www.who.int/teams/global-tuberculosis-programme/tb-guidelines
[3]	Guidelines for the Treatment of Latent Tuberculosis Infection, Centers for Disease Control and Prevention of America, 2016. Available from: https://www.cdc.gov/tb/topic/treatment/ltbi.htm
[4]	S. Jitsinchayakul, R. Zarin, A. Khan, A. Yusuf, G. Zaman, U. W. Humphries, et al., Fractional modeling of COVID-19 epidemic model with harmonic mean type incidence rate, Open Phys., 19 (2021), 693–709. https://doi.org/10.1515/phys-2021-0062 doi: 10.1515/phys-2021-0062
[5]	R. Zarin, Numerical study of a nonlinear COVID-19 pandemic model by finite difference and meshless methods, Partial Differ. Equ. Appl. Math., 6 (2022), 100460. https://doi.org/10.1016/j.padiff.2022.100460 doi: 10.1016/j.padiff.2022.100460
[6]	Z. Raizah, R. Zarin, Advancing COVID-19 understanding: Simulating omicron variant spread using fractional-order models and haar wavelet collocation, Mathematics, 11 (2023), 1925. https://doi.org/10.3390/math11081925 doi: 10.3390/math11081925
[7]	R. Zarin, U. W. Humphries, T. Saleewong, Advanced mathematical modeling of hepatitis B transmission dynamics with and without diffusion effect using real data from Thailand, Eur. Phys. J. Plus, 139 (2024), 385. https://doi.org/10.1140/epjp/s13360-024-05154-7 doi: 10.1140/epjp/s13360-024-05154-7
[8]	K. Guedri, R. Zarin, A. Zeb, B. M. Makhdoum, H. A. Niyazi, A. Khan, A numerical study of HIV/AIDS transmission dynamics and the onset of long-term disability in chronic infection, Eur. Phys. J. Plus, 139 (2024), 1127. https://doi.org/10.1140/epjp/s13360-024-05881-x doi: 10.1140/epjp/s13360-024-05881-x
[9]	K. Guedri, R. Zarin, M. Oreijah, S. K. Alharbi, H. A. E. W. Khalifa, Artificial neural network-driven modeling of Ebola transmission dynamics with delays and disability outcomes, Comput. Biol. Chem., 115 (2025), 108350. https://doi.org/10.1016/j.compbiolchem.2025.108350 doi: 10.1016/j.compbiolchem.2025.108350
[10]	R. Zarin, Artificial neural network-based approach for simulating influenza dynamics: A nonlinear SVEIR model with spatial diffusion, Eng. Anal. Bound. Elem., 176 (2025), 106230. https://doi.org/10.1016/j.enganabound.2025.106230 doi: 10.1016/j.enganabound.2025.106230
[11]	M. Alqhtani, K. M. Saad, R. Zarin, A. Khan, W. M. Hamanah, Qualitative behavior of a highly non-linear Cutaneous Leishmania epidemic model under convex incidence rate with real data, Math. Biosci. Eng., 21 (2024), 2084–2120. http://doi.org/10.3934/mbe.2024092 doi: 10.3934/mbe.2024092
[12]	S. Alqahtani, A. Kashkary, A. Asiri, H. Kamal, J. Binongo, K. Castro, et al., Impact of mobile teams on tuberculosis treatment outcomes, Riyadh Region, Kingdom of Saudi Arabia, 2013–2015, J. Epidemiol. Glob. Health, 7 (2017), S29–S33. https://doi.org/10.1016/j.jegh.2017.09.005 doi: 10.1016/j.jegh.2017.09.005
[13]	O. Nave, Y. Shor, R. Bar, E. E. Segal, M. Sigron, A new treatment for breast cancer using a combination of two drugs: AZD9496 and palbociclib, Sci. Rep., 14 (2024), 1307. https://doi.org/10.1038/s41598-023-48305-z doi: 10.1038/s41598-023-48305-z
[14]	N. Zhang, X. Wang, W. Li, Stability for multi-linked stochastic delayed complex networks with stochastic hybrid impulses by Dupire Itô's formula, Nonlinear Anal. Hybrid Syst., 45 (2022), 101200. https://doi.org/10.1016/j.nahs.2022.101200 doi: 10.1016/j.nahs.2022.101200
[15]	N. Zhang, Z. Wang, J. H. Park, W. Li, Semi-global synchronization of stochastic mixed time-delay systems with Lévy Noise under aperiodic intermittent delayed sampled-data control, Automatica, 171 (2025), 111963. https://doi.org/10.1016/j.automatica.2024.111963 doi: 10.1016/j.automatica.2024.111963
[16]	N. Zhang, S. Huang, L. Ning, W. Li, Semi-global sampling control for semi-Markov jump systems with distributed delay, IEEE Trans. Autom. Sci. Eng., 21 (2024), 3603–3614. https://doi.org/10.1109/TASE.2023.3282053 doi: 10.1109/TASE.2023.3282053
[17]	R. G. White, G. P. Garnett, Mathematical modelling of the epidemiology of tuberculosis, Infect. Dis. Clin., 24 (2010), 825–841. https://doi.org/10.1007/978-1-4419-6064-1 doi: 10.1007/978-1-4419-6064-1
[18]	H. T. Waaler, A. Geser, S. Andersen, The use of mathematical models in the study of the epidemiology of tuberculosis, Am. J. Public Health, 52 (1962), 1002–1013.
[19]	Y. Li, J. Wang, Y. Zhao, A dynamical model of tuberculosis with media impact, J. Epidemiol., 17 (2022), 235–243.
[20]	A. Das, S. Rana, A. Kumar, Media impact on the spread of tuberculosis: A mathematical model, Infect. Dis. Model., 5 (2020), 327–338.
[21]	C. Bhunu, W. Garira, Z. Mukandavire, G. Magombedze, Modeling the effects of vaccination on the transmission dynamics of tuberculosis, Infect. Dis. Model., 3 (2008), 190–200.
[22]	D. Okuonghae, P. L. Omosigho, Mathematical modeling of tuberculosis: vaccination and drug resistance, Math. Biosci., 220 (2011), 21–36.
[23]	C. Castillo-Chavez, Z. Feng, Mathematical models for the transmission dynamics of tuberculosis, Math. Biosci., 151 (1997), 135–154.
[24]	C. Dye, B. G. Williams, Criteria for the control of drug-resistant tuberculosis, Proc. Natl. Acad. Sci. USA, 97 (2000), 8180–8185. https://doi.org/10.1073/pnas.140102797 doi: 10.1073/pnas.140102797
[25]	C. Ozcaglar, A. Shabbeer, S. L. Vandenberg, B. Yener, K. P. Bennett, Epidemiological models of Mycobacterium tuberculosis complex infections, Math. Biosci., 236 (2012), 77–96. https://doi.org/10.1016/j.mbs.2012.02.003 doi: 10.1016/j.mbs.2012.02.003
[26]	Y. Wang, B. Xu, Z. Zhang, Epidemiological impact and mathematical analysis of drug-resistant tuberculosis, J. Infect. Dis., 41 (2023), 112–124.
[27]	P. Duve, S. Charles, J. Munyakazi, R. Lühken, P. Witbooi, A mathematical model for malaria disease dynamics with vaccination and infected immigrants, Math. Biosci. Eng., 21 (2024), 1082–1109. http://doi.org/10.3934/mbe.2024045 doi: 10.3934/mbe.2024045
[28]	W. Walter, Ordinary differential equations, Berlin: Springer Science & Business Media, 2013.
[29]	M. W. Hirsch, S. Smale, R. L. Devaney, Discrete dynamical systems, In: Differential equations, eynamical systems, and an introduction to chaos, New York: Academic Press, 2013,329–359. https://doi.org/10.1016/b978-0-12-382010-5.00015-4
[30]	P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48. https://doi.org/10.1016/S0025-5564(02)00108-6 doi: 10.1016/S0025-5564(02)00108-6
[31]	Y. Li, X. Liu, Y. Yuan, J. Li, L. Wang, Global analysis of tuberculosis dynamical model and optimal control strategies based on case data in the United States, Appl. Math. Comput., 422 (2022), 126983. https://doi.org/10.1016/j.amc.2022.126983 doi: 10.1016/j.amc.2022.126983
[32]	Y. Wu, M. Huang, X. Wang, Y. Li, L. Jiang, Y. Yuan, The prevention and control of tuberculosis: an analysis based on a tuberculosis dynamic model derived from the cases of Americans, BMC Public Health, 20 (2020), 1173. https://doi.org/10.1186/s12889-020-09260-w doi: 10.1186/s12889-020-09260-w
[33]	J. Zhang, Y. Li, X. Zhang, Mathematical modeling of tuberculosis data of China, J. Theor. Biol., 365 (2015), 159–163. https://doi.org/10.1016/j.jtbi.2014.10.019 doi: 10.1016/j.jtbi.2014.10.019
[34]	Y. Ma, C. R. Horsburgh Jr, L. F. White, H. E. Jenkins, Quantifying TB transmission: a systematic review of reproduction number and serial interval estimates for tuberculosis, Epidemiol. Infect., 146 (2018), 1478–1494. https://doi.org/10.1017/S0950268818001760 doi: 10.1017/S0950268818001760
[35]	Incidence of tuberculosis in Saudi Arabia, World Bank, 2023. Available from: https://data.worldbank.org/indicator/SH.TBS.INCD?locations = SA
[36]	J. C. Butcher, Numerical methods for ordinary differential equations, Hoboken: Wiley, 2016.
[37]	E. Hairer, S. P. Nørsett, G. Wanner, Solving ordinary differential equations I: nonstiff problems, 2 Eds., Berlin: Springer, 1993.
[38]	L. F. Shampine, S. Thompson, Solving DDEs in MATLAB, Appl. Numer. Math., 37 (2001), 441–458. https://doi.org/10.1016/S0168-9274(00)00055-6 doi: 10.1016/S0168-9274(00)00055-6
[39]	U. M. Ascher, L. R. Petzold, Computer methods for ordinary differential equations and differential-algebraic equations, Philadelphia: SIAM, 1998.
[40]	A. Bellen, M. Zennaro, Numerical methods for delay differential equations, Oxford: Oxford University Press, 2003.

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