A study about mathematical analysis of Hepatitis B virus using Optimal Control approach
Main Article Content
Abstract
This research focuses on the mathematical modeling of Hepatitis B virus (HBV) dynamics using optimal control theory to enhance understanding of transmission patterns and optimize intervention strategies. An ordinary differential equation (ODE) model is proposed, capturing the dynamics of HBV transmission through distinct compartments: susceptible, exposed, infected, liver cirrhosis, and removed. Advanced liver cirrhosis, a severe stage of chronic liver disease caused by sustained and progressive damage, has emerged as a critical non-communicable health concern. The study employs mathematical simulations to analyze the impact of various control measures in mitigating HBV spread. Through the application of optimal control theory and the Hamiltonian principle, the research identifies effective strategies, such as vaccination, treatment, and awareness campaigns, to manage and limit HBV transmission. The primary objective is to minimize the number of individuals in the infected and cirrhotic stages while reducing associated intervention costs. By targeting HBV, a leading cause of cirrhosis, the study aims to lower the incidence of chronic liver disease. The findings highlight the importance of vaccination, effective treatment protocols, and public awareness in curbing the progression of HBV and reducing its long-term health impacts. This research provides crucial insights for public health policies and the development of targeted strategies to combat HBV and its complications.
Downloads
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- 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.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
References
] Samanta, G. P., & Sharma, S. (2014). Analysis of a delayed Chlamydia epidemic model with pulse vaccination. Applied Mathematics and Computation, 230, 555-569.
] Livingston, S. E., Simonetti, J. P., McMahon, B. J., Bulkow, L. R., Hurlburt, K. J., Homan, C. E., ... & Chulanov, V. P. (2007). Hepatitis B virus genotypes in Alaska Native people with hepatocellular carcinoma: preponderance of genotype F. The Journal of infectious diseases, 195(1), 5-11.
] McMahon, B. J., Alberts, S. R., Wainwright, R. B., Bulkow, L., & Lanier, A. P. (1990). Hepatitis B–related sequelae: prospective study in 1400 hepatitis B surface antigen–positive Alaska native carriers. Archives of internal medicine, 150(5), 1051-1054.
] World Health Organization, Hepatitis B, 2018. Available from: https://www.who.int/newsroom/fact-sheets/detail/hepatitis-B.
] China Center for Disease Control and Prevention, Questions and answers on hepatitis B vaccination,2013. http://www.chinacdc.cn/zxdt/201312/t20131230 92034.htm.
] Akyuz, F., Kaymakoglu, S., Demir, K., Aksoy, N., Karaca, C., Danalioglu, A., ... & Okten, A. (2007). Lamivudine monotherapy and lamivudine plus interferon alpha combination therapy in HBeAg negative chronic hepatitis B not responding to previous interferon alpha monotherapy. Acta Gastro-Enterologica Belgica, 70(1).
] Schiff, E. R., Dienstag, J. L., Karayalcin, S., Grimm, I. S., Perrillo, R. P., Husa, P., ... & International Lamivudine Investigator Group. (2003). Lamivudine and 24 weeks of lamivudine/interferon combination therapy for hepatitis B e antigen-positive chronic hepatitis B in interferon nonresponders. Journal of hepatology, 38(6), 818-826.
] Wodajo, F. A., & Mekonnen, T. T. (2022). Mathematical model analysis and numerical simulation of intervention strategies to reduce transmission and re-activation of hepatitis B disease. F1000Research, 11(931), 931.
] Wang, L. Y., You, S. L., Lu, S. N., Ho, H. C., Wu, M. H., Sun, C. A., ... & Chen, C. J. (2003). Risk of hepatocellular carcinoma and habits of alcohol drinking, betel quid chewing and cigarette smoking: a cohort of 2416 HBsAg-seropositive and 9421 HBsAg-seronegative male residents in Taiwan. Cancer Causes & Control, 14, 241-250.
] Zhang T, Wang K, Zhang X. Modeling and analyzing the transmission dynamics of HBV epidemic in Xinjiang, China. PloS One 2015;10(9):e0138765.
] Anderson, R. (1991). Infectious diseases of humans: dynamics and control. Cambridge Univer-sity Press.
] Zhao, S., Xu, Z., & Lu, Y. (2000). A mathematical model of hepatitis B virus transmission and its application for vaccination strategy in China. International journal of epidemiology, 29(4), 744-752.
] Wilt, T. J., Shamliyan, T., Shaukat, A., Taylor, B. C., MacDonald, R., Yuan, J. M., ... & Kane, R. L. (2008). Management of chronic hepatitis B. Evidence report/technology assessment, (174), 1-671.
] Khan, T., Zaman, G., & Chohan, M. I. (2017). The transmission dynamic and optimal control of acute and chronic hepatitis B. Journal of biological dynamics, 11(1), 172-189.
] Rezaul Karim, Pinakee Dey, Md. Mijanoor Rahman, Sanjay Kumar Saha, Md. Shafiqul Islam, Md. Nazmul Hossain, Majid Khan Majahar Ali. (2022). A Study about Forecasting Bangladesh by Using Verhulst Logistic Growth Model and Population Model. Annals of the Romanian Society for Cell Biology, 26(01), 566–578.Retrievedfrom,https://www.annalsofrscb.ro/index.php/journal/article/view/10845
] 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.
] Rezaul Karim, Mohammad Asif Arefin, Md. Mosharof Hossain, Md. Shahidul Islam. Investigate future population projection of Bangladesh with the help of Malthusian model, Sharpe-lotka model and Gurtin Mac-Camy model. Int J Stat Appl Math 2020;5(5):77-83. DOI: 10.22271/maths.2020.v5.i5b.585.
] Mondal, M. K., Hanif, M., & Biswas, M. H. A. (2017). A mathematical analysis for controlling the spread of Nipah virus infection. International Journal of Modelling and Simulation, 37(3), 185-197.
] Wodajo, F. A., Gebru, D. M., & Alemneh, H. T. (2023). Mathematical model analysis of effective intervention strategies on transmission dynamics of hepatitis B virus. Scientific Reports, 13(1), 8737.
] Wodajo, F. A., Gebru, D. M., & Alemneh, H. T. (2023). Mathematical model analysis of effective intervention strategies on transmission dynamics of hepatitis B virus. Scientific Reports, 13(1), 8737.
] Rezaul Karim,M. A. Bkar Pk,Md. Asaduzzaman,Pinakee Dey,M. Ali Akbar. Investigation on predicting family planning and women’s and children’s health effects on bangladesh by conducting age structure population model. doi:https://doi.org/10.26782/jmcms.2024.03.00005
] Ja Khan, T., Zaman, G., & Algahtani, O. (2015). Transmission dynamic and vaccination of hepatitis B epidemic model. WULFENIA J, 22(2), 230-241.ouad and Karam, “Mathematical analysis and treatment for a delayed Hepatitis B viral infectionmodel with the adaptive,” Published: 19 November 2018. Immune Response and DNA-ContainingCapsids.
] Wasley, A., & Alter, M. J. (2000). Epidemiology of hepatitis C: geographic differences and temporal trends. In Seminars in liver disease (Vol. 20, No. 01, pp. 0001-0016). Copyright© 2000 by Thieme Medical Publishers, Inc., 333 Seventh Avenue, New York, NY 10001, USA. Tel.:+ 1 (212) 584-4663.
] Vinter, R. B., & Vinter, R. B. (2010). Optimal control (Vol. 2, No. 1). Boston: Birkhäuser.
] Karim, R., Pk, M. B., Dey, P., Akbar, M. A., & Osman, M. S. (2024). A study about the prediction of population growth and demographic transition in Bangladesh. Journal of Umm Al-Qura University for Applied Sciences, 1-13. https://doi.org/10.1007/s43994-024-00150-0
] Mimi, M. A., Ali, M. E., & Roy, K. C. (2023). Analyze the growth rate of a prey-predator system with simulation using matlab. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 14(03), 480-497.