Dynamical Analysis and Optimal Control of SVIR Hepatitis B Model Spread in Malang
DOI:
https://doi.org/10.30736/voj.v5i2.698Keywords:
Stability Analysis, Optimal Control, HBV Epidemic Model, Saturated Incidence Rate, Numerical SimulationAbstract
This research formulates a new mathematical model that describes the dynamics of the spread and control of Hepatitis B, especially in Malang, East Java. The mathematical model that will be constructed considers various factors in Malang, mainly the saturated Incidence rate and vaccinations carried out on newborns. The equilibrium point of the system is determined and its stability is dynamically analized. The results of this analysis will determine the future prediction of the spread of Hepatitis B in Malang. Furthermore, a control strategy is proposed that is Clean and Healthy Living behavior (PHBS). The control strategy is analysed using optimal control theory. Pontryagin’s principle is used as a condition to obtain optimal conditions. Forward-backwards Sweep method in combination with the fourth order Runge-Kutta method is used to solve the optimal system.
Downloads
References
Alligood, K. T., Sauer, T. D., & Yorke, J. A. (2000). An Introduction to dynamical system. New York: Springer-Verlag.
Aulani, F., Kusumawinahyu, W. M., & Darti, I. (2021). Dynamical Analysis and Parameter Estimation of a Model of Hepatitis B Disease Spread in Malang. The Journal of Experimental Life Science, XI (3), 84-88.
Darajat, P. P., & Husadaningsih, T. (2019). Kontrol Optimal Pada Model Penyebaran Virus Komputer dengan Klasifikasi Pengamanan. E-Jurnal Matematika, 8(4), 253-258.
Darajat, P. P., Suryanto, A., & Widodo, A. (2016). Optimal Control On The Spread of SLBS Computer Virus Model. International Journal of Pure and Apllied Mathematic, 107(3), 749-758.
Djilali, S., & Bentout, S. (2021). Global dynamics of SVIR epidemic model with distributed delay and imperfect vaccine. Results in Physics, 25(104245), 1-7.
Golgeli, M. (2019). A Mathematical Model Of Hepatitis B Transmission In Turkey. Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics, 68(2), 1586-1595.
Kesehatan, K. (2012). Hepatitis Masalah Kesehatan Dunia. Kementerian Kesehatan RI.
Kesehatan, K. (2014). Situasi dan Analisis Hepatitis, INFODATIN: Pusat Data dan Informasi Kementerian Kesehatan RI. Kementerian Kesehatan RI.
Khan, T., Ullah, Z., Ali, N., & Zaman, G. (2019). Modeling and control of the hepatitis B virus spreading using an epidemic model. Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena(124), 1-9.
Khan, T., Zaman, G., & Chohan, M. I. (2018). The transmission dynamic of different hepatitis B-infected individuals with the effect of hospitalization. JOURNAL OF BIOLOGICAL DYNAMICS, XII(1), 611-631.
Lenhart, S., & Workman, J. T. (2015). Optimal Control Apllied to Biological Models. New York: Taylor and Francis.
Murray, J. D. (2002). Mathematical Biology: An Introduction to Dynamical System . Berlin: Springer-Verlag.
Oke, M. O., Ogunmiloro, O. M., Akinwumi, C. T., & Raji, R. A. (2019). Mathematical Modeling and Stability Analysis of a SIRV Epidemic Model with Non-linear Force of Infection and Treatment. Communications in Mathematics and Applications, X(4), 717-731.
Pertiwi, M. D. (2020). Distribusi Kejadian Hepatitis B Menurut Cakupan Imunisasi HB-0 dan Cakupan K4 Di Jawa Timur. Jurnal Ikesma, 16(1), 36-44.
S. Tsukuda, K. W. (2020). “Hepatitis B virus biology and life cycleâ€. Antiviral Research, 182(104925), 1-10.
Zhang, Z., & Upadhyay, R. K. (2021). Dynamical analysis for a deterministic SVIRS epidemic model with Holling type II incidence rate and multiple delays. Results in Physics, XXIV(104181), 1-13.
Downloads
Published
How to Cite
Issue
Section
License
Copyright:
Authors who publish their manuscripts in this Journal agree to the following conditions:
- Copyright of any article on Vygotsky: Jurnal Pendidikan Matematika dan Matematika is held solely by the author under the Creative Commons Attribution 4.0 International license (CC BY NC SA).
- Authors can submit papers separately, arrange non-exclusive distribution of manuscripts that have been published in this journal into other versions (e.g. sending to the author's institutional repository, publication in a book, etc.) by acknowledging that the manuscript has been published for the first time in Vygotsky: Jurnal Pendidikan Matematika dan Matematika.
License:
Vygotsky: Jurnal Pendidikan Matematika dan Matematika is published under the terms of the Creative Commons Attribution 4.0 International License (CC BY NC SA). This license permits anyone to copy and redistribute this material in any form or format, compile, modify and develop this material for any purpose as long as it is not for commercial purposes. Additionally, anyone must provide credit and distribute contributions under the license of the creator of the original work.