Optimal Control Model for Hepatitis B Virus

• Authors: Martins Onyekwelu Onuorah , Abdulahi Mohammed Baba , Nanangwe Alaisa , Robert Ssali Balagadde , Inncent Kabandana
• Languages of publication: EN

Abstracts

EN

In this paper, we proposed an ordinary differential equation model for the transmission of Hepatitis B virus (BHV). The model accounted for the susceptible, exposed, infected, Chronic, and removed classes. We obtained the model's disease-free and endemic equilibrium points and the effective reproductive number. Further, from a thorough sensitivity analysis of the effective reproductive number, we extended the model by incorporating five time-dependent controls to cater to the vertical transmission, vaccination, testing, and treatment of acutely and chronically infected individuals. Numerical simulation was conducted to underscore the effects of the control in combating HBV.

Keywords

EN

Hepadnaviridea; Hepatitis; Hepatitis B virus; Lebesques measurable; Pointwise hamiltonian; differential equation; equilibrium; optimal control; simulation; stability

Discipline

• INFORMATICS: INFORMATICS

• Publisher: Scientific Publishing House „DARWIN”
• Journal: World News of Natural Sciences
• Year: 2023
• Volume: 48
• Pages: 70-94

Contributors

author

Martins Onyekwelu Onuorah

• Department of Mathematics & Statistics, School of Mathematics and Computing, Kampala International University, Main Campus, Kampala, Uganda

author

Abdulahi Mohammed Baba

• Department of Mathematics & Statistics, School of Mathematics and Computing, Kampala International University, Main Campus, Kampala, Uganda

author

Nanangwe Alaisa

• Department of Education Science, Faculty of Education Open and Distance E-Learning, Kampala International University, Main Campus, Kampala, Uganda

author

Robert Ssali Balagadde

• Department of Computer Science, School of Mathematics and Computing, Kampala International University, Main Campus, Kampala, Uganda

author

Inncent Kabandana

• Department of Computer Science, College of Science and Technology (CST), School of ICT, University of Rwanda, Kigali, Rwanda

References

• [1] Abdullahi, M. B., Hasan, Y. A., & Abdullah, F. A. (2015). Control of Plasmodium knowlesi malaria. AIP Conference Proceedings, 1682. https://doi.org/10.1063/1.4932444
• [2] Alrabaiah, H., Safi, M. A., DarAssi, M. H., Al-Hdaibat, B., Ullah, S., Khan, M. A., & Ali Shah, S. A. (2020). Optimal control analysis of hepatitis B virus with treatment and vaccination. Results in Physics, 19, 1–16. https://doi.org/10.1016/j.rinp.2020.103599
• [3] Aniji, M., Kavitha, N., & Balamuralitharan, S. (2020). Mathematical modeling of hepatitis B virus infection for antiviral therapy using LHAM. Advances in Difference Equations, 2020(408), 1–19. https://doi.org/10.1186/s13662-020-02770-2
• [4] Asfaw Wodajo, F., & Tibebu Mekonnen, T. (2022). Mathematical model analysis and numerical simulation of intervention strategies to reduce transmission and reactivation of hepatitis B disease. F1000Research, 11(931), 1–28. https://doi.org/10.12688/f1000research.124234.1
• [5] Aziz ur Rehman, M., Kazim, M., Ahmed, N., Raza, A., Rafiq, M., Akgül, A., Inc, M., Park, C., & Zakarya, M. (2023). Positivity preserving numerical method for epidemic model of hepatitis B disease dynamic with delay factor. Alexandria Engineering Journal, 64, 505–515. https://doi.org/10.1016/j.aej.2022.09.013
• [6] Dano, L. B., Rao, K. P., & Keno, T. D. (2022). Modeling the Combined Effect of Hepatitis B Infection and Heavy Alcohol Consumption on the Progression Dynamics of Liver Cirrhosis. Journal of Mathematics, 2022, 1–18. https://doi.org/10.1155/2022/6936396
• [7] Din, A., & Abidin, M. Z. (2022). Analysis of fractional-order vaccinated Hepatitis-B epidemic model with Mittag-Leffler kernels. Mathematical Modelling and Numerical Simulation With Applications, 2(2), 59–72. https://doi.org/10.53391/mmnsa.2022.006
• [8] Din, A., & Li, Y. (2022). Mathematical analysis of a new nonlinear stochastic hepatitis B epidemic model with vaccination effect and a case study. European Physical Journal Plus, 137(558), 1–24. https://doi.org/10.1140/epjp/s13360-022-02748-x
• [9] Din, A., Li, Y., & Shah, M. A. (2021). The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control. Journal of Systems Science and Complexity, 34(4), 1301–1323. https://doi.org/10.1007/s11424-021-0053-0
• [10] Driessche, P. van den, & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48.
• [11] Elkhadir, S. H., Saeed, A. E. M., & Abasher, A. (2022). Mathematical Model of Hepatitis B Virus With Effect of Vaccination and Treatments. International Journal of Analysis and Applications, 20(53), 1–16. https://doi.org/10.28924/2291-8639-20-2022-53
• [12] Emechebe, G., Emodi, I., Ikefuna, A., Ilechukwu, G., Igwe, W., & Ejiofor, O. (2009). Hepatitis B virus infection in Nigeria-A review. Niger Med J, 50(18).
• [13] Fatehi, F., Bingham, R. J., Stockley, P. G., & Twarock, R. (2022). An age-structured model of hepatitis B viral infection highlights the potential of different therapeutic strategies. Scientific Reports, 12(1252), 1–12. https://doi.org/10.1038/s41598-021-04022-z
• [14] Hethcotet, H. W. (2000). The Mathematics of Infectious. SIAM Review, 42(4), 599–653.
• [15] Khatun, M. S., & Biswas, M. H. A. (2020). Optimal control strategies for preventing hepatitis B infection and reducing chronic liver cirrhosis incidence. Infectious Disease Modelling, 5, 91–110. https://doi.org/10.1016/j.idm.2019.12.006
• [16] Kiire, C. (1993). The epidemiology and control of hepatitis B in sub-Saharan Africa. The Epidemiology and Control of Hepatitis B in Sub-Saharan Africa 40, 141–156.
• [17] Ma, J., & Ma, S. (2023). Dynamics of a stochastic hepatitis B virus transmission model with media coverage and a case study of China. Mathematical Biosciences and Engineering, 20(2), 3070–3098. https://doi.org/10.3934/mbe.2023145
• [18] Manna, K., & Hattaf, K. (2022). A generalized distributed delay model for hepatitis B virus infection with two modes of transmission and adaptive immunity: A mathematical study. Mathematical Methods in the Applied Sciences, 45(17), 11614–11634. https://doi.org/10.1002/mma.8470
• [19] Means, S., Ali, M. A., Ho, H., & Heffernan, J. (2020). Mathematical Modeling for Hepatitis B Virus: Would Spatial Effects Play a Role and How to Model It? Frontiers in Physiology, 11(146), 1–5. https://doi.org/10.3389/fphys.2020.00146
• [20] Nicolini, L., Orsi, A., Tatarelli, P., Viscoli, C., Icardi, G., & Sticchi, L. (2019). A global view to HBV chronic infection: Evolving strategies for diagnosis, treatment and prevention in immunocompetent individuals. Int J Environ Res Public Health, 16 (3307).
• [21] Okosun, K. O., Khan, M. A., Bonyah, E., & Okosun, O. O. (2019). Cholera-schistosomiasis coinfection dynamics. Optimal Control Applications and Methods, 40(4), 703–727. https://doi.org/10.1002/oca.2507
• [22] Osman, S., Otoo, D., & Makinde, O. D. (2020). Modeling Anthrax with Optimal Control and Cost Effectiveness Analysis. Applied Mathematics, 11(03), 255–275. https://doi.org/10.4236/am.2020.113020
• [23] Schmit, N., Nayagam, S., Lemoine, M., Ndow, G., Shimakawa, Y., Thursz, M. R., & Hallett, T. B. (2023). Cost-effectiveness of different monitoring strategies in a screening and treatment programme for hepatitis B in The Gambia. Journal of Global Health, 13(04004), 1–11. https://doi.org/10.7189/jogh.13.04004
• [24] Schweitzer, A., Horn, J., Mikolajczyk, R., Krause, G., & Ott, J. (2015). Estimations of worldwide prevalence of chronic hepatitis B virus infection: A systematic review of data published between 1965 and 2013. Lancet, 386(1546–1555).
• [25] Searles, R., Xu, L., Killian, W., Vanderbruggen, T., Forren, T., Howe, J., Pearson, Z., Shannon, C., Simmons, J., & Cavazos, J. (2017). Parallelization of Machine Learning Applied to Call Graphs of Binaries for Malware Detection. Proceedings - 2017 25th Euromicro International Conference on Parallel, Distributed and Network-Based Processing, PDP 2017, 69–77. https://doi.org/10.1109/PDP.2017.41
• [26] Side, S., Abdy, M., Arwadi, F., & Sanusi, W. (2021). SEIRI Model analysis using the mathematical graph as a solution for Hepatitis B disease in Makassar. Journal of Physics: Conference Series, 1899(1). https://doi.org/10.1088/1742-6596/1899/1/012091
• [27] Volinsky, I. (2022). Mathematical Model of Hepatitis B Virus Treatment with Support of Immune System. Mathematics, 10(2821), 1–11. https://doi.org/10.3390/math10152821
• [28] Volinsky, I., Lombardo, S. D., & Cheredman, P. (2021). Stability analysis of a mathematical model of hepatitis b virus with unbounded memory control on the immune system in the neighborhood of the equilibrium free point. Symmetry, 13(166). https://doi.org/10.3390/sym13081437
• [29] Yavuz, M., Özköse, F., Susam, M., & Kalidass, M. (2023). A New Modeling of Fractional-Order and Sensitivity Analysis for Hepatitis-B Disease with Real Data. Fractal and Fractional, 7(165), 1–24. https://doi.org/10.3390/fractalfract7020165
• [30] Zada, I., Naeem Jan, M., Ali, N., Alrowail, D., Sooppy Nisar, K., & Zaman, G. (2021). Mathematical analysis of hepatitis B epidemic model with optimal control. Advances in Difference Equations, 2021(451), 1–29. https://doi.org/10.1186/s13662-021-03607-2

• Document Type: article