Abstract
In this paper, we ameliorate the model proposed in [13], by incorporating the influence of hepatitis B e antigen (HBeAg) status of mothers on vertical transmission. We use the improved model to fit reported HBV new infections in the Zhejiang Province of China. Also to predict the course of the Hepatitis B (HBV) infection in this Chinese area, and in Tokombere, located in sub-Saharan Africa(SSA). Furthermore, we apply optimal control techniques in view to re-examine the effects of the newborn vaccination, the universal vaccination and the treatment of chronic carriers in preventing the HBV infection. Simulation results show that treatment slightly steps in the optimal strategy, while immunisation is an effective measure. On the other hand, they indicate that the control measures and immunization programs implemented in Zhejiang Province are effective. Besides, they suggest that in SSA, a package of several policies centred on birth dose vaccination should be implemented.
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J Amin, M G L Law, M Bartlett, J L Kaldor, G J L Dore. Causes of death after diagnosis of hepatitis b or hepatitis c infection: a large community-based linkage study, The Lancet, 2006, 368(9539): 938–945.
G Borgia, M A Carleo, G B Gaeta, I Gentile. Hepatitis b in pregnancy, World Journal of Gastroenterology: WJG, 2012, 18(34): 4677.
J Dionne-Odom, B Njei, A T N Tita. Elimination of vertical transmission of hepatitis b in africa: a review of available tools and new opportunities, Clinical therapeutics, 2018, 40(8): 1255–1267.
J Dionne-Odom, A O Westfall, D Nzuobontane, M J Vinikoor, G Halle-Ekane, T Welty, A T N Tita. Predictors of infant hepatitis b immunization in cameroon: data to inform implementation of a hepatitis b birth dose, The pediatric infectious disease journal, 2018, 37(1): 103–107.
EASL, et al. EASL 2017 Clinical Practice Guidelines on the management of hepatitis b virus infection, Journal of Hepatology, 2017.
W J Edmunds, G F Medley, D J Nokes. The transmission dynamics and control of hepatitis b virus in the gambia, Statistics in medicine, 1996, 15(20): 2215–2233.
W Fleming, R Rishel. Deterministic and stochastic optimal control, Springer New York, 2012, https://doi.org/10.1007/978-1-4612-6380-7.
A A B Frambo, J Atashili, P N Fon, P M Ndumbe. Prevalence of hbsag and knowledge about hepatitis b in pregnancy in the buea health district, cameroon: a cross-sectional study, BMC research notes, 2014, 25(7):394, DOI: https://doi.org/10.1186/1756-0500-7-394.
J K Ghosh, U Ghosh, M H A Biswas, S Sarkar. Qualitative analysis and optimal control strategy of an sir model with saturated incidence and treatment, Differential Equations and Dynamical Systems, 2023, 31(1): 53–67.
S T Goldstein, F Zhou, S C Hadler, B P Bell, E E Mast, H S Margolis. A mathematical model to estimate global hepatitis b disease burden and vaccination impact, International Journal of Epidemiology, 2005, 34(6): 1329–1339.
B Gomero. Latin hypercube sampling and partial rank correlation coefficient analysis applied to an optimal control problem. Master’s thesis, University of Tennessee, Knoxville, 1962.
S Hahné, M Ramsay, K Balogun, W J Edmunds, P Mortimer. Incidence and routes of transmission of hepatitis b virus in england and wales, 1995–2000: implications for immunisation policy, Journal of Clinical Virology, 2004, 29(4): 211–220.
J P II Kouenkam, J Mbang, Y Emvudu. Global dynamics of a model of hepatitis b virus infection in a sub-saharan african rural area, International Journal of Biomathematics, 2020, 13(6): 2050054.
Y Jia, L Li, F Cui, D Zhang, G Zhang, F Wang, X Gong, H Zheng, Z Wu, N Miao, et al. Cost-effectiveness analysis of a hepatitis b vaccination catch-up program among children in shandong province, china, Human vaccines & immunotherapeutics, 2014, 10(10): 2983–2991.
A S Kadi, P H Sahana, G Muleta. An optimal control approach to transmission dynamics of hepatitis b virus, Indian Journal of Applied Research, 2017, 7: 36–39.
A V Kamyad, R Akbari, A A Heydari, A Heydari. Mathematical modeling of transmission dynamics and optimal control of vaccination and treatment for hepatitis b virus, Computational and Mathematical Methods in Medicine, 2014, 2014: 475451, DOI: https://doi.org/10.1155/2014/475451.
A U Kaoje, Y Mohammed, M O Raji, H S Bala, S Garba, H M Garba, et al. Public awareness, knowledge and vaccination status against hepatitis b infection among residents of sokoto metropolisnigeria, J Hepat Res, 2018, 4(1): 1035.
M A Khan, S Islam, J C Valverde, S A Khan. Control strategies of hepatitis b with three control variables, Journal of Biological Systems, 2018, 26(1): 1–21.
M A Khan, S A A Shah, S Ullah, K O Okosun, M Farooq. Optimal control analysis of the effect of treatment, isolation and vaccination on hepatitis b virus, Journal of Biological Systems, 2020, 282(2): 351–376.
T Khan, G Zaman, M I Chohan. The transmission dynamic and optimal control of acute and chronic hepatitis b, Journal of biological dynamics, 2017, 11(1): 172–189.
M S Khatun, M H A Biswas. Optimal control strategies for preventing hepatitis b infection and reducing chronic liver cirrhosis incidence, Infectious Disease Modelling, 2020, 5: 91–110.
D E Landoh, F Ouro-Kavalah, I Yaya, A L Kahn, P Wasswa, A Lacle, D I Nassoury, S N Gitta, A B Soura. Predictors of incomplete immunization coverage among one to five years old children in togo, BMC Public Health, 2016, 16(1): 968, DOI: https://doi.org/10.1186/s12889-016-3625-5.
S Lenhart, J T Workman. Optimal control applied to biological models, CRC press, 2007.
Y F Liaw, M R Brunetto, S Hadziyannis. The natural history of chronic hbv infection and geographical differences, Antiviral Therapy, 2010, 15(3): 25–33.
M Loriette, J Birguel, R Damza, M Ratoua, S Karsikam, J J Sobnangou, C Aurenche, F Lunel-Fabiani, J M Huraux. Une expérience de lutte contre l’hépatite b en zone rurale à l’extrême nord du cameroun, Médecine et Santé Tropicales, 2015, 25(4): 422–427.
S Marino, I B Hogue, C J Ray, D E Kirschner. A methodology for performing global uncertainty and sensitivity analysis in systems biology, Journal of theoretical biology, 2008, 254(1): 178–196.
G F Medley, N A Lindop, W J Edmunds, D J Nokes. Hepatitis-b virus endemicity: heterogeneity, catastrophic dynamics and control, Nature medicine, 2001, 7(5): 619–24.
N Miao, H Zheng, X Sun, L Shen, F Wang, F Cui, Z Yin, G Zhang, F Wang. Enhanced sentinel surveillance for hepatitis b infection in 200 counties in china, 2013–2016, PloS one, 2019, 14(4): e0215580.
G A O’Hara, A L McNaughton, T Maponga, P Jooste, P Ocama, R Chilengi, J Mokaya, M I Liyayi, T Wachira, D M Gikungi, et al. Hepatitis b virus infection as a neglected tropical disease, PLoS neglected tropical diseases, 2017, 11(10): e0005842.
J Pang, J Cui, X Zhou. Dynamical behavior of a hepatitis b virus transmission model with vaccination, Journal of Theoretical Biology, 2010, 265(4): 572–578.
L S Pontryagin, V G Boltyanskii, R V Gamkrelidze, E F Mishchenko. The mathematical theory of optimal processes, translated by kn trirogoff, New York, 1962.
C W Spearman, M Afihene, R Ally, B Apica, Y Awuku, L Cunha, G Dusheiko, N Gogela, C Kassianides, M Kew, et al. Hepatitis b in sub-saharan africa: strategies to achieve the 2030 elimination targets, The lancet gastroenterology & hepatology, 2017, 2(12): 900–909.
C E Stevens, P Toy, S Kamili, P E Taylor, M J Tong, G L **a, G N Vyas. Eradicating hepatitis b virus: the critical role of preventing perinatal transmission, Biologicals, 2017, 50: 3–19.
S Ullah, M A Khan, J F Gómez-Aguilar. Mathematical formulation of hepatitis b virus with optimal control analysis, Optimal Control Applications and Methods, 2019, 40(3): 529–544.
P V D Driessche, J Watmough. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical biosciences, 2002, 180(1): 29–48.
E Villa, G Fattovich, A Mauro, M Pasino. Natural history of chronic hbv infection: special emphasis on the prognostic implications of the inactive carrier state versus chronic hepatitis, Digestive and Liver Disease, 2011, 43: S8–S14.
Z Wang, Y Chen, J Pan. Trends of acute hepatitis b notification rates in eastern china from 2005 to 2013, PloS one, 2014, 9(12): e114645.
J R Williams, D J Nokes, G F Medley, R M Anderson. The transmission dynamics of hepatitis b in the uk: a mathematical model for evaluating costs and effectiveness of immunization programmes, Epidemiology & Infection, 1996, 116(1): 71–89.
WHO, et al. Global Health Observatory (GHO) data 2015, Retrieved, 2015, 3: 23.
WHO, et al. Global health sector strategy on viral hepatitis 2016–2021. towards ending viral hepatitis, Technical report, World Health Organization, 2016.
Y P Yan, H X Su, Z H Ji, Z J Shao, Z S Pu. Epidemiology of hepatitis b virus infection in china: current status and challenges, Journal of clinical and translational hepatology, 2014, 2(1): 15–22.
H J Yim, A S F Lok. Natural history of chronic hepatitis b virus infection: What we knew in 1981 and what we know in 2005, Hepatology, 2006, 43(S1): S173–81.
G H Zacharakis, J Koskinas, S Kotsiou, M Papoutselis, F Tzara, N Vafeiadis, A J Archimandritis, K Papoutselis. Natural history of chronic hbv infection: A cohort study with up to 12 years follow-up in north greece (part of the interreg i–ii/ec-project), Journal of medical virology, 2005, 77(2): 173–179.
J Zhang, S Zhang. Application and optimal control for an hbv model with vaccination and treatment, Discrete Dynamics in Nature and Society, 2018, 2018: 1–13.
L Zou, W Zhang, S Ruan. Modeling the transmission dynamics and control of hepatitis b virus in china, Journal of Theoretical Biology, 2010, 262(2): 330–338.
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Kouenkam, J.P., Mbang, J., Chendjou, G. et al. Optimal Control of Hepatitis B in a sub-Saharan African rural area. Appl. Math. J. Chin. Univ. 38, 523–544 (2023). https://doi.org/10.1007/s11766-023-4332-5
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DOI: https://doi.org/10.1007/s11766-023-4332-5