Article Sidebar

Download
PDF (فارسی)
Statistic
Read Counter : 67 Download : 34

Main Article Content

Abstract

Mathematical models of diseases, which study the mechanisms of disease transmission and control from a mathematical perspective, play a significant role in assisting public health policymakers in designing strategies for disease control. In this paper, two mathematical models of tuberculosis, SEIR and SVEIL, are analyzed and compared. Various aspects of the models, such as their structure, stability analysis, basic reproduction number, differences in variables and parameters, and scope of application, are evaluated. We demonstrated that the SVEIL model is more comprehensive than the SEIR model; it incorporates vaccination and successful treatment, and the loss of immunity against the disease, offering a more realistic analysis of disease dynamics. However, due to its expanded structure, the SVEIL model involves greater computational complexity in conducting stability analysis and calculating the basic reproduction number.

Keywords

Basic Reproduction Number Comparison Mathematical Models Stability of Equilibrium Points Tuberculosis

Article Details

License

Copyright (c) 2025 Reserved for Kabul University

Creative Commons License

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

Author Biographies

Dr. Noorullah Noori, Department of Mathematics, Kabul University, Kabul, Af

د ریاضیاتو څانګه ، د ریاضیاتو پوهنځی، کابل پوهنتون، کابل، افغانستان

Dr. Abdul Wakil Baidar, Department of Mathematics, Kabul University, Kabul, Af

د ریاضیاتو څانګه ، د ریاضیاتو پوهنځی، کابل پوهنتون، کابل، افغانستان

How to Cite
Takal, M. H., Noori, N., & Baidar, A. W. (2025). Comparison of the Structures of SEIR and SVEIL Mathematical Models of Tuberculosis. Journal of Natural Sciences – Kabul University, 8(2), 103–119. https://doi.org/10.62810/jns.v8i2.444
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. Antunes, J. L. F., & Waldman, E. A. (2001). The impact of AIDS, immigration and housing overcrowding on tuberculosis deaths in São Paulo, Brazil, 1994–1998. Social Science & Medicine, 52(7), 1071–1080. https://doi.org/10.1016/S0277-9536(00)00214-8 DOI: https://doi.org/10.1016/S0277-9536(00)00214-8
  2. Brady, R., & Enderling, H. (2019). Mathematical Models of Cancer: When to Predict Novel Therapies, and When Not to. Bulletin of Mathematical Biology, 81(10), 3722–3731. https://doi.org/10.1007/S11538-019-00640 DOI: https://doi.org/10.1007/s11538-019-00640-x
  3. Chinnathambi, R., Rihan, F. A., & Alsakaji, H. J. (2021). A fractional-order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections. Mathematical Methods in the Applied Sciences, 44(10), 8011–8025. https://doi.org/10.1002/MMA.5676 DOI: https://doi.org/10.1002/mma.5676
  4. Ginting, E., Aldila, D., & Febiriana, I. H. (2024). A deterministic compartment model for analyzing tuberculosis dynamics considering vaccination and reinfection. Healthcare Analytics, 5, 100341. https://doi.org/10.1016/J.HEALTH.2024.100341 DOI: https://doi.org/10.1016/j.health.2024.100341
  5. Diekmann, O., Heesterbeek, J. A. P., & Metz, J. A. J. (1990). On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28(4), 365–382. https://doi.org/10.1007/BF00178324/METRICS DOI: https://doi.org/10.1007/BF00178324
  6. Driessche, P. Van Den, & Watmough, J. (n.d.). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. March 2005, 1–21.
  7. Jia, Z.-W., Tang, G.-Y., Jin, Z., Dye, C., Vlas, S. J., Li, X.-W., Feng, D., Fang, L.-Q., Zhao, W.-J., & Cao, W.-C. (2008). Modeling the impact of immigration on the epidemiology of tuberculosis. Elsevier, 73, 437–448. https://doi.org/10.1016/j.tpb.2007.12.007 DOI: https://doi.org/10.1016/j.tpb.2007.12.007
  8. Mengistu, A., & Witbooi, P. J. (2019). Modeling the Effects of Vaccination and Treatment on Tuberculosis Transmission Dynamics. Journal of Applied Mathematics, 2019. https://doi.org/10.1155/2019/7463167 DOI: https://doi.org/10.1155/2019/7463167
  9. Kereyu, D., & Demie, S. (2021). Transmission dynamics model of Tuberculosis with optimal control strategies in Haramaya district, Ethiopia. Advances in Difference Equations, 2021(1), 1–22. https://doi.org/10.1186/S13662-021 DOI: https://doi.org/10.1186/s13662-021-03448-z
  10. Khan, M. A., Ahmad, M., Ullah, S., Farooq, M., & Gul, T. (2019). Modeling the transmission dynamics of tuberculosis in Khyber Pakhtunkhwa Pakistan. Advances in Mechanical Engineering, 11(6). https://doi.org/10.1177/1687814019854835 DOI: https://doi.org/10.1177/1687814019854835
  11. Kucharski, A. J., Russell, T. W., Diamond, C., Liu, Y., Edmunds, J., Funk, S., Eggo, R. M., Sun, F., Jit, M., Munday, J. D., Davies, N., Gimma, A., van Zandvoort, K., Gibbs, H., Hellewell, J., Jarvis, C. I., Clifford, S., Quilty, B. J., Bosse, N. I., … Flasche, S. (2020). Early dynamics of transmission and control of COVID-19: a mathematical modelling study. The Lancet Infectious Diseases, 20(5), 553–558. https://doi.org/10.1016/S1473 DOI: https://doi.org/10.1016/S1473-3099(20)30144-4
  12. Mandal, S., Sarkar, R., & Sinha, S. (2011). Mathematical models of malaria - A review. Malaria Journal, 10(1), 1–19. https://doi.org/10.1186/1475-2875 DOI: https://doi.org/10.1186/1475-2875-10-202
  13. NOORANI, M. S. M. (2012). SEIR MODEL FOR TRANSMISSION OF DENGUE FEVER IN SELANGOR MALAYSIA. International Journal of Modern Physics: Conference Series, 9, 380. https://doi.org/10.1142/S2010194512005454 DOI: https://doi.org/10.1142/S2010194512005454
  14. Trauer, J. M., Denholm, J. T., & McBryde, E. S. (2014). Construction of a mathematical model for tuberculosis transmission in highly endemic regions of the Asia-pacific. Journal of Theoretical Biology, 358, 74–84. https://doi.org/10.1016/j.jtbi.2014.05.023 DOI: https://doi.org/10.1016/j.jtbi.2014.05.023
  15. Twumasi, C., Asiedu, L., & Nortey, E. N. N. (2019). Markov Chain Modeling of HIV, Tuberculosis, and Hepatitis B Transmission in Ghana. Interdisciplinary Perspectives on Infectious Diseases, 2019. https://doi.org/10.1155/2019/9362492 DOI: https://doi.org/10.1155/2019/9362492
  16. Ucakan, Y., Gulen, S., & Koklu, K. (2021a). Analysing of Tuberculosis in Turkey through SIR, SEIR and BSEIR Mathematical Models. Mathematical and Computer Modelling of Dynamical Systems, 27(1), 179–202. https://doi.org/10.1080/13873954.2021.1881560
  17. Ucakan, Y., Gulen, S., & Koklu, K. (2021b). Analysing of Tuberculosis in Turkey through SIR, SEIR and BSEIR Mathematical Models. Mathematical and Computer Modelling of Dynamical Systems, 27(1), 179–202. https://doi.org/10.1080/13873954.2021.1881560 DOI: https://doi.org/10.1080/13873954.2021.1881560
  18. Ullah, I., Ahmad, S., & Zahri, M. (2023). Investigation of the effect of awareness and treatment on Tuberculosis infection via a novel epidemic model. Alexandria Engineering Journal, 68, 127–139. https://doi.org/10.1016/j.aej.2022.12.061 DOI: https://doi.org/10.1016/j.aej.2022.12.061
  19. WAALER, H., GESER, A., & ANDERSEN, S. (1962). The use of mathematical models in the study of the epidemiology of tuberculosis. American Journal of Public Health and the Nation’s Health, 52(6), 1002–1013. https://doi.org/10.2105/AJPH.52.6.1002 DOI: https://doi.org/10.2105/AJPH.52.6.1002
  20. WHO. (2023). Tuberculosis. Link
  21. WHO. (2024). Global Tuberculosis Report. Link
  22. Widyaningsih, P., Nugroho, A. A., Saputro, D. R. S., & Sutanto. (2019). Tuberculosis transmission with relapse in Indonesia: susceptible vaccinated infected recovered model. Journal of Physics: Conference Series, 1217(1), 012071. https://doi.org/10.1088/1742 DOI: https://doi.org/10.1088/1742-6596/1217/1/012071
  23. Yang, Y., Li, J., Ma, Z., Chaos, L. L.-, Fractals, S. &, & 2010, undefined. (n.d.). Global stability of two models with incomplete treatment for tuberculosis. ElsevierY Yang, J Li, Z Ma, L LiuChaos, Solitons & Fractals, 2010•Elsevier. Retrieved March 6, 2025, from Link
  24. Zhao, K., Liu, Z., Guo, C., Xiang, H., Liu, L., & Wang, L. (2025). Modeling and analysis of transmission dynamics of tuberculosis with preventive treatment and vaccination strategies in China. Applied Mathematical Modelling, 138, 115779. https://doi.org/10.1016/J.APM.2024.115779 DOI: https://doi.org/10.1016/j.apm.2024.115779
  25. Zhao, Y., Li, M., & Yuan, S. (2017). Analysis of transmission and control of tuberculosis in Mainland China, 2005-2016, based on the age-structure mathematical model. International Journal of Environmental Research and Public Health, 14(10). https://doi.org/10.3390/ijerph14101192 DOI: https://doi.org/10.3390/ijerph14101192