mmnsa Mathematical Modelling and Numerical Simulation with Applications 2791-8564 Mehmet YAVUZ 10.53391/mmnsa.1528691 Biological Mathematics Dynamical Systems in Applications Biyolojik Matematik Uygulamalarda Dinamik Sistemler Mathematical modelling of the impact of vaccination, treatment and media awareness on the hepatitis B epidemic in Burkina Faso https://orcid.org/0000-0002-4791-7567 Kiemtore Adama LANIBIO Laboratory University Joseph Ki-Zerbo, 03 BP 7021, Ouagadougou https://orcid.org/0000-0003-3028-0886 Sawadogo Wenddabo Olivier LARED Laboratory University of Bernard Lédéa Ouédraogo 01 BP 346 Ouahigouya https://orcid.org/0009-0003-6080-4940 Ouédraogo Pegdwindé Ousséni Fabrice LaST Laboratory, University of Thomas Sankara, 12 BP 417 Ouagadougou 12 https://orcid.org/0000-0002-5633-0311 Aqel Fatima Computer, Networks, Mobility and Modeling Laboratory (IR2M), Faculty of Sciences and Technics, Hassan First University, Settat 26000 https://orcid.org/0000-0002-6367-311X Alaa Hamza LAMAI Laboratory, Faculty of Sciences and Technology, University of Cadi Ayyad, Abdelkrim, Khattabi, Marrakech 40000 https://orcid.org/0000-0002-2422-1866 Somda Kounpielime Sosthène Department of Gastroenterology, Yalgado Ouedraogo University Hospital, 01 BP 5234, Ouagadougou 01 https://orcid.org/0000-0002-8173-2179 Serme Abdel Karim Department of Gastroenterology, Yalgado Ouedraogo University Hospital, 01 BP 5234, Ouagadougou 01 12 31 2024 4 5-Special Issue: ICAME'24 139 164 08 08 2024 12 27 2024 Copyright © 2021, Mathematical Modelling and Numerical Simulation with Applications 2021 Mathematical Modelling and Numerical Simulation with Applications

Infection with the hepatitis B virus (HBV) remains a global public health issue. Particularly in Burkina Faso, HBV is a major public health concern due to its high prevalence and associated mortality. However, universal vaccination, treatment of chronic carriers, and awareness campaigns are currently employed means in Burkina Faso to combat the spread of HBV. Therefore, this paper aims to study the impact of these control measures on the expansion of this virus. This paper presents a mathematical model of vertically transmitted HBV that takes into account the progression to chronicity as a function of the age of the infected person, as well as vaccination, treatment of chronic carriers, and media awareness. After formulating the model and carrying out the mathematical analysis, we simulated the proposed model in Matlab, taking into account the various involved parameters. Finally, we presented the results of sensitivity analysis and numerical simulation. According to our model, with vaccination coverage of $30\%$, a $50\%$ success rate of awareness campaigns and $20\%$ effectiveness for the $10\%$ of treated chronic carriers, the prevalence of hepatitis B infection could decrease down to $2\%$ within thirty years in Burkina Faso.

 Hepatitis B effective reproduction number sensitivity analysis vaccination No financial support [1] World Health Organization, Progress report on HIV, viral hepatitis and sexually transmitted infections 2019: accountability for the global health sector strategies, 2016-2021. World Health Organization, (2019). [2] Ministère de la Santé. Normes et Protocoles de Prise en Charge des Hépatites Virales au Burkina Faso, (2019). Ministère de la santé du Burkina Faso, https://scge-cm.com/download. [3] Masseta, M. Incidental discovery of HBs antigen at the Y.O. University Hospital: socio-demographic, clinical and paraclinical aspects, PhD Thesis, Joseph Ki-Zerbo University, (2018). [4] Banach, M. (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 Collaborator. The Lancet Gastroenterology and Hepatology, 7(9), 796 -829, (2022). [5] Ott, J.J., Stevens, G.A., Groeger, J. and Wiersma, S.T. Global epidemiology of hepatitis B virus infection: new estimates of age-specific HBsAg seroprevalence and endemicity. Vaccine, 30(12), 2212-2219, (2012). [6] Ministry of Health, Burkina. Hepatitis B, cirrhosis and primary liver cancer kill nearly 5,000 people a year by Editorial Board, Ouagadougou, Fasozine, (2017). https://fasozine.com. [7] Meda, N., Tuaillon, E., Kania, D., Tiendrebeogo, A., Pisoni, A., Zida, S., ... and Dujols, P. Hepatitis B and C virus seroprevalence, Burkina Faso: a cross-sectional study. Bulletin of the World Health Organization, 96(11), 750, (2018). [8] Zouré, A.A., Nadembega, C., Ouattara, A.K., Traoré, L., Tiemtoré, A., Sawadogo, O., ... and Simpore, J. State of the HIV, Hepatitis B and C Virus Pandemic from 2003 to 2022 in Burkina Faso: Evolution of Prevalence Trends and Strategic Recommendations to Achieve the WHO’s Goal for Their Eradication by 2030. Advances in Infectious Diseases Scientific Research Publishing, 14(3) 628–643 (2024). [9] Tao, I., Compaoré, T.R., Diarra, B., Djigma, F., Zohoncon, T.M., Assih, M., ... and Simpore, J. Seroepidemiology of hepatitis B and C viruses in the general population of Burkina Faso. Hepatitis Research and Treatment, 2014(1), 781843, (2014). [10] Guingané, A.N., Kaboré, R., Shimakawa, Y., Somé, E.N., Kania, D., Pisoni, A., ... and Tuaillon, E. Screening for Hepatitis B in partners and children of women positive for surface antigen, Burkina Faso. Bulletin of the World Health Organization, 100(4), 256, (2022). [11] Somé, E.N., Kaboré, J., Kaboré, C., Somda, S., Somé, R., Somda, P. and Sombié, R. Burkina Faso and the global goal of eliminating Hepatitis B virus By 2030. Advances in Public Health, Community and Tropical Medicine, 2022(02), 1-5, (2022). [12] Kiemtoré, A., Sawadogo, W.O., Aquel, F., Alaa, H. and Somda, K.S. Mathematical modelling and Numerical Simulation of Hepatitis B Viral Infection: the case of Burkina Faso. European Journal of Pure and Applied Mathematics, 17(1), 59–92 (2024). [13] Feld, J., Janssen, H.L., Abbas, Z., Elewaut, A., Ferenci, P., Isakov, V., ... and LeMair, A. World gastroenterology organisation global guideline hepatitis B: September 2015. Journal of Clinical Gastroenterology, 50(9), 691–703, (2016). [14] Fall, A., Iggidr, A., Sallet, G. and Tewa, J.J. Epidemiological models and Lyapunov functions. Mathematical Modelling of Natural Phenomena, 2(1), 62-83, (2007). [15] Bonzi, B., Fall, A.A., Iggidr, A. and Sallet, G. Stability of differential susceptibility and infectivity epidemic models. Journal of Mathematical Biology, 62(1), 39-64, (2011). [16] Kiemtore, A., Sawadogo, W.O., Zangré, I., Ouedraogo, P.O.F. and Mouaouia, I. Estimation of parameters for the mathematical model of the spread of hepatitis B in Burkina Faso using grey wolf optimizer. International Journal of Analysis and Applications, 22, 48-48, (2024). [17] Anderson, R.M. and May, R.M. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press: New York, (1991). [18] Edmunds, W.J., Medley, G.F., Nokes, D.J., O’callaghan, C.J., Whittle, H.C. and Hall, A.J. Epidemiological patterns of hepatitis B virus (HBV) in highly endemic areasr. Epidemiology & Infection, 117(2), 313-325, (1996). [CrossRef] [19] Mahardika, D., Tjahjana, R. and Sunarsih, S. Dynamic modelling of Hepatitis B and use of optimal control to reduce the infected population and minimizing the cost of vaccination and treatment. In Proceedings, AIP Conference Proceedings, (Vol. 2331, No. 1), pp. 020013, Jakarta, Indonesia, (2021, April). [20] Sanz-Bueno, J., Vanaclocha, F. García-Doval, I., Torrado, R., Carretero, G., Daudén, E. et al. Risk of reactivation of hepatitis B virus infection in psoriasis patients treated with biologics: a retrospective analysis of 20 cases from the BIOBADADERM database. Actas DermoSifiliográficas (English Edition), 106(6), 477-482, (2015). [21] Aqel, F., Alaa, H. and Alaa, N.E. Mathematical model of Covid-19 transmissibility during the vaccination period. Eurasian Journal of Mathematical and Computer Applications, 11(1), 4-28, (2023). [22] Seidu, B., Bornaa, C.S. and Makinde, O.D. An Ebola model with hyper-susceptibility. Chaos, Solitons & Fractals, 138, 109938, (2020). [23] Van den Driessche, P. and Watmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1- 2), 29-48, (2002). [24] Peter, O.J., Abidemi, A., Fatmawati, F., Ojo, M.M. and Oguntolu, F.A. Optimizing tuberculosis control: a comprehensive simulation of integrated interventions using a mathematical model. Mathematical Modelling and Numerical Simulation with Applications, 4(3), 238-255, (2024). [25] Mamo, T.T. and Mekonnen, T.T. An age structure mathematical model analysis on the dynamics of chronic and hyper toxic forms of hepatitis B virus by model with vaccination intervention control strategy in Ethiopia. International Journal of Sciences Basic and Applied Research (IJSBAR), 50(1), 106-136, (2020). [26] Latifah, M.L. and Helma. Mathematical model of vertical transmission of hepatitis B with the effect of treatment and vaccination. Rangkiang Mathematics Journal, 2(2), 20-29, (2023). [27] Delamater, P.L., Street, E.J., Leslie, T.F., Yang, Y.T. and Jacobsen, K.H. Complexity of the basic reproduction number (R0). Emerging Infectious Diseases, 25(1), 1-4, (2019). [28] Inglesby, T.V. Public health measures and the reproduction number of SARS-CoV-2. Jama, 323(21), 2186-2187, (2020). [29] Castillo-Chavez, C., Blower, S., Van den Driessche, P., Kirschner, D. and Yakubu, A.A. Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory (Vol. 126). Springer: New York, (2002). [30] Castillo-Chavez, C., Feng, Z. and Huang W. On the computation of R0 and its role on global stability. Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction (pp. 229-250). New York: Springer, (2002). [31] Khan, A., Zarin, R., Ahmed, I., Yusuf, A. and Humphries, U.W. Numerical and theoretical analysis of Rabies model under the harmonic mean type incidence rate. Results in Physics, 29, 104652, (2021). [32] Castillo-Chavez, C. and Feng, Z. Global stability of an age-structure model for TB and its applications to optimal vaccination strategies. Mathematical Biosciences, 151(2), 135-154, (1998). [33] Dai, C., Fan, A. and Wang, K. Transmission dynamics and the control of hepatitis B in China: a population dynamics view. Journal of Applied Analysis and Computation, 6(1), 76-93, (2016). [34] McCluskey, C.C. Global stability of an SIR epidemic model with delay and general nonlinear incidence. Mathematical Biosciences and Engineering, 7(4), 837-850, (2010). [35] Koutou, O. and Sangaré, B. Mathematical analysis of the impact of the media coverage in mitigating the outbreak of COVID-19. Mathematics and Computers in Simulation, 205, 600-618, (2023). [36] Duan, X., Yuan, S. and Li, X. Global stability of an SVIR model with age of vaccination. Applied Mathematics and Computation, 226, 528-540, (2014). [37] Lasalle, J.P. The Stability of Dynamical Systems. SIAM: Philadelphia, (1976). [38] Din, A., Li, Y. and Shah, M.A. The complex dynamics of hepatitis B infected individuals with optimal control. Journal of Systems Science and Complexity, 34(4), 1301-1323, (2021). [39] Bounkaicha, C., Allali, K., Tabit, Y. and Danane, J. Global dynamic of spatio-temporal fractional order SEIR model. Mathematical Modeling and Computing, 10(2), 299-310 (2023). [40] Lakshmikantham, V., Leela, S. and Martynyuk, A.A. Stability Analysis of Nonlinear Systems. Marcel Dekker: New York, (1989). [41] Asamoah, J.K.K., Jin, Z. and Sun, G.Q. Non-seasonal and seasonal relapse model for Q fever disease with comprehensive cost-effectiveness analysis. Results in Physics, 22, 103889, (2021). [42] Norton, J. An introduction to sensitivity assessment of simulation models. Environmental Modelling & Software, 69, 166-174, (2015). [43] Mirjalili, S., Mirjalili, S.M. and Lewis, A. Grey wolf optimizer. Advances in Engineering Software, 69, 46-61, (2014). [44] INSD, General population and housing census, Burkina Faso, 2019. Fifth General Census of Population and Housing of Burkina Faso, Synthesis of final results, (2022). https://insd.bf/ [45] Edmunds, W.J., Medley, G.F. and Nokes, D.J. The transmission dynamics and control of hepatitis B virus in The Gambia. Statistics in Medicine, 15(20), 2215-2233, (1996). [46] Lu, F.T. and Ni, Y.H. Elimination of mother-to-infant transmission of hepatitis B virus: 35 years of experience. Pediatric Gastroenterology, Hepatology & Nutrition, 23(4), 311-318, (2020).