Dynamical analysis of HIV-TB co-infection transmission model in the presence of treatment for TB
DOI:
https://doi.org/10.59292/bulletinbiomath.2024002Keywords:
Tuberculosis, HIV, co-infection, symptoms, stability, simulationsAbstract
The immense disease burden of tuberculosis (TB) infection is well-documented, particularly among those co-infected with HIV and TB. To better understand the transmission dynamics of HIV-TB co-infection in the absence of readily available HIV treatment, we develop a deterministic compartmental co-infection model. Our model helps to identify the effects of TB infection on the co-infection dynamics of the two diseases, especially when treatment for TB is readily available. We find that susceptibility to TB reinfection after a previous infection leads to backward bifurcation in the TB-only model when the associated reproduction number (R_0) is less than unity. However, when we make the susceptibility to TB re-infection insignificant in the model, the disease-free equilibrium of the TB-only model is locally asymptotically stable when the associated R_0 is less than unity. We conduct sensitivity and uncertainty analyses to identify the key parameters driving TB infection dynamics, using the R_0 as the response function. We discover that the transmission rate for TB, the modification parameters accounting for the infectiousness of infected individuals with TB-only, and the treatment rates for singly infected individuals with latently infected TB are the top drivers of TB infection in the given population. Our numerical simulations suggest that concentrating treatment on TB-infected individuals in the diagnosed latently infected stage (singly or dually infected with HIV) could effectively reduce the co-infection disease burden and HIV incidence in the population under study.
References
Azeez, A., Ndege, J., Mutambayi, R. and Qin, Y. A mathematical model for TB/HIV co-infection in treatment and transmission mechanism. Asian Journal of Mathematics and Computer Research, 22(4), 180-192, (2017).
David, J.F. Mathematics epidemiology of HIV/AIDS and tuberculosis co-infection. Ph.D. Thesis, Department of Mathematics, Faculty of Sciences, University of British Columbia, (2015).
Silva, C.J. and Torres, D.F.M. Modeling TB-HIV syndemic and treatment. Journal of Applied Mathematics, 2014, 248407, (2014).
Agbata, B.C, Ode, O.J., Ani, B.N., Odo, C.E. and Olorunishola O.A. Mathematical assessment of the transmission dynamics of HIV/AIDS with treatment effects. International Journal of Mathematics and Statistics Studies (IJMSS), 7(4), 40-52, (2019).
Chun, T.W. and Fauci, A.S. HIV reservoirs: pathogenesis and obstacles to viral eradication and cure. Aids, 26(10), 1261-1268, (2012).
World Health Organization (WHO), Tuberculosis, (2023). https://www.who.int/news-room/fact-sheets/detail/tuberculosis, [Accessed: 11/02/2024].
Agbata, B.C., Omale, D., Ojih, P.B. and Omatola, I.U. Mathematical analysis of Chickenpox transmission dynamics with control measures. Continental Journal of Applied Sciences, 14(2), 6-23, (2019).
Centre for Disease Control (CDC), Basic TB facts, (2016). https://www.cdc.gov/tb/topic/basics/default.htm, [Accessed: 11/02/2024].
Shah, N.H. and Gupta, J. Mathematical modelling of pulmonary and extra-pulmonary tuberculosis. International Journal of Mathematics Trends and Technology, 4(9), 158-162, (2013).
World Health Organization (WHO), Global tuberculosis report, (2023). https://www.who.int/teams/global-tuberculosis-programme/tb-reports, [Accessed: 19/08/2023].
Mitku, A.A., Dessie, Z.G., Muluneh, E.K. and Workie, D.L. Prevalence and associated factors of TB/HIV co-infection among HIV infected patients in Amhhara region Ethiopia. African Health Sciences, 16(2), 588-595, (2016).
Wang, X., Yang, J. and Zhang, F. Dynamic of a TB-HIV coinfection epidemic model with latent age. Journal of Applied Mathematics, 2013, 429567, (2013).
Kaur, N., Ghosh, M. and Bhatia, S.S. HIV-TB co-infection: a simple mathematical model. Journal of Advanced Research in Dynamical and Control Systems, 7(1), 66-81, (2015).
Fatmawati and Tasman, H. An optimal treatment control of TB-HIV coinfection. International Journal of Mathematics and Mathematical Sciences, 2016, 8261208, (2016).
Omale, D., Ojih, P.B., Atokolo, W., Omale, A.J and Bolaji, B. Mathematical model for transmission dynamics of HIV and tuberculosis co-infection in Kogi State, Nigeria. Journal of Mathematical and Computational Science, 11(5), 5580-5613, (2021).
Nwankwo, A. and Okuonghae, D. Mathematical analysis of the transmission dynamics of HIV syphilis co-infection in the presence of treatment for syphilis. Bulletin of Mathematical Biology, 80, 437-492, (2018).
Agbata, B.C., Emmanuel, O., Bashir, T. and William, O. Mathematical analysis of COVID-19 transmission dynamics with a case study of Nigeria and its computer simulation. medRxiv, (2020).
Diekman, O. and Heesterbeck, J.A.P. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. John Wiley & Sons: New York, (2000).
Naresh, R., Sharma, D. and Tripathi, A. Modelling the effect of tuberculosis on the spread of HIV infection in a population with density-dependent birth and death rate. Mathematical and Computer Modelling, 50(7-8), 1154-1166, (2009).
Van den Driessche, P. and Watmough, J. Reproduction number and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1-2), 29–48, (2002).
Naim, M., Sabbar, Y. and Zeb, A. Stability characterization of a fractional-order viral system with the non-cytolytic immune assumption. Mathematical Modelling and Numerical Simulation with Applications, 2(3), 164-176, (2022).
Sabbar, Y., Din, A. and Kiouach, D. Influence of fractal–fractional differentiation and independent quadratic Lévy jumps on the dynamics of a general epidemic model with vaccination strategy. Chaos, Solitons & Fractals, 171, 113434, (2023).
Ammi, M.R.S., Zinihi, A., Raezah, A.A. and Sabbar, Y. Optimal control of a spatiotemporal SIR model with reaction–diffusion involving p-Laplacian operator. Results in Physics, 106895, (2023).
Odionyenma, U.B., Omame, A., Ukanwoke, N.O. and Nometa, I. Optimal control of Chlamydia model with vaccination. International Journal of Dynamics and Control, 10, 332-348, (2022).
Omame, A., Okuonghae, D., Nwafor, U.E. and Odionyenma, B.U. A co-infection model for HPV and syphilis with optimal control and cost-effectiveness analysis. International Journal of Biomathematics, 14(07), 2150050, (2021).
Blower, S.M. and Dowlatabadi, H. Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example. International Statistical Review/Revue Internationale de Statistique, 62(2), 229–243, (1994).
Okuonghae, D. and Omosigho, S.E. Analysis of a mathematical model for tuberculosis: what could be done to increase case detection. Journal of Theoretical Biology, 269(1), 31–45, (2011).
Gumel, A.B. Causes of backward bifurcations in some epidemiological models. Journal of Mathematical Analysis and Applications, 395(1), 355-365, (2012).
Iboi, E. and Okuonghae, D. Population dynamics of a mathematical model for syphilis. Applied Mathematical Modelling, 40(5-6), 3573–3590, (2016).
Castillo-Chavez, C. and Song, B. Dynamical models of tuberculosis and their applications. Mathematical Biosciences and Engineering, 1(2), 361–404, (2004).
Sanchez, M.A. and Blower, S.M. Uncertainty and sensitivity analysis of the basic reproductive rate: tuberculosis as an example. American Journal of Epidemiology, 145(12), 1127–1137, (1997).
Elbasha, E.H. Model for hepatitis C virus transmission. Mathematical Biosciences and Engineering, 10(4), 1045–1065, (2013).
Ridzon, R., Gallagher, K., Ciesielski, C., Mast, E.E., Ginsberg, M.B., Robertson, B.J. et al. Simultaneous transmission of human immunodeficiency virus and hepatitis C virus from a needle-stick injury. The New England Journal of Medicine, 336(13), 919–922, (1997).
La Salle, J.P. and Lefschetz, S. The stability of dynamical systems. SIAM: Philadelphia, (1976).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Bolarinwa Bolaji, Thomas Onoja, Celestine Agbata, Benjamin Idoko Omede, Udoka Benedict Odionyenma
This work is licensed under a Creative Commons Attribution 4.0 International License.
Articles published in the Bulletin of Biomathematics are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in the Bulletin of Biomathematics, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.