Control of Transmission of Hepatitis B Disease with Vaccination, Campaign, and Treatment

A Ika Putriani(1*), Syamsuddin Toaha(2),

(1) Universitas Hasanuddin, Indonesia
(2) FMIPA Universitas Hasanuddin, Indonesia
(*) Corresponding Author




DOI: https://doi.org/10.26858/jdm.v10i2.35882

Abstract


Hepatitis B disease is an inflammatory liver disease caused by the hepatitis B virus and can cause liver cirrhosis, cancer, and liver failure. This study discusses the optimal control mathematical model of the dynamics of the spread of hepatitis B. This model consists of six population compartments, namely susceptible to infection with hepatitis B or  Susceptible, Exposed,  infected with acute hepatitis B or Acute Infected , infected with chronic hepatitis B or Chronic Infected, suffering from liver cirrhosis or Liver Cirrhotic, and infected who are recovering or Removed. The system is solved by using Pontryagin's minimum principle and numerically by the forward-backward sweep method. Numerical simulation of the optimal control  shows that with vaccination , campaign on hepatitis B, and treatment, the spread of hepatitis B can be eradicated more quickly. The implementation large amounts of vaccination, campaign on hepatitis B, and treatment  need to be carried out from the start and the proportion can be reduced until a certain time is no longer necessary. The use of controls in the form of vaccinations, campaigns on hepatitis B, and treatment  needs to be carried out for a longer time to prevent the spread of hepatitis B infection. 


Keywords


Hepatitis B, Mathematical Model, Optimal Control, Pontryagin Minimum Principle, Forward-Backward Sweep

References


Alrabaiah, H.,Safi MA, Darassi MH, dkk.2020. Optimal control analysis of hepatitis B virus with

treatment and vaccination. Result in Physics.

B-Symptoms, causes Mayo Clinic, http://www.mayoclinic.org/ diseases- conditions / hepatitis-

b/symptoms- causes/syc-20366802

Dirac MA,2022, Global, regional, and national burden of hepatitis B, 1990-2019: a systematic analysis for the global burden of disease study 2019, GBD 2019 Hepatitis B Collarators

Farida, Yeni, Andayani, TM, Ratnasari, N., 2014. Analisis Penggunaan Obat pada Komplikasi Sirosis Hati, Jurnal Manajemen dan Pelayanan Farmasi, Vol. 4(2), 77-84.

H. B-Symptoms, causes Mayo Clinic,http://www.mayoclinic.org/diseases-conditions/hepatitis-b/symptoms-causes/syc-20366802

Khan, MA, Islam, S., dan Zaman, G., 2018. Media coverage campaign in Hepatitis B transmission

model, Apllied Mathematics and Computation,Vol. 331, 378 – 393.

Khatun, MS, Biswas, MHA, 2020. Optimal Control Strategies for Preventing Hepatitis B Infection and Reducing Chronic Liver CirrHosis Incidence. Infectious Disease Modeling, Vol.5 , 91-110.

Lavanchy D. Hepatitis B virus epidemiology, disease burden, treatment, and current and emerging prevention and control measures. J Viral Hepatitis 2004;11 (2):97–107.

Sun Z, Ming L, Zhu X, Lu J. Prevention and control of hepatitisB in China. J Med Virol 2002;67(3):447–50.

Supu, NA, Saltina, Palalu, K., Ismail, R. 2021. Model epidemi SICKR pada penyebaran penyakit hepatitis B dan kanker hati. Gorontalo: Universitas Negeri Gorontalo.

Toaha, S. & Rustam., 2017. Optimal Harvesting Policy of Predator-Prey Model with Free Fishing and Reserve Zones. AIP Conference Proceedings Vol. 1825 02002.

WH Organization, World Health Organization (WHO) Media Centre. Available: Accessed 2018 February 12; 2018.

Zhang, J., Suxia, Z., 2018. Application and Optimal Control for an HBV Model with Vaccination and Treatment. Hindawi, Vol.2018, 1-13.


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