Simulation on The Mathematical Model for the Control Of Hepatitis B Virus-Hepatitis D Virus (HBV-HDV) Co-infection Transmission Dynamics in a Given Population

Yıl 2021, Cilt: 4 Sayı: 2, 72 - 88, 31.08.2021

Remigius Okeke Aja Titus Chinebu Godwin Mbah

https://doi.org/10.33187/jmsm.943746

Öz

This paper investigates the impact of the various parameters of the mathematical model for Hepatitis B virus-Hepatitis D virus (HBV-HDV) co-infection with controls (awareness, vaccine and therapy). It establishes that the model is biologically meaningful and epidemiologically well posed. Furthermore, simulations are carried out on the equations of the model using MATLAB and the results indicate that; when $c_1$(awareness) increase from $0.08$ to $0.70$, then the number of exposed HB individuals in the population will also increase. Conversely, we notice a drastic decrease in the number of exposed HBD individuals in the population when $c_1$(awareness) increase from $0.08$ to $0.70$. Again, we observe a decrease in the number of exposed treated individuals in the population when $c$(therapy) increase from $0.08$ to $0.50$. Similarly, we notice an increase in the number of recovered HBD individuals in the population upon the increase of $c$(therapy) from $0.08$ to $0.50$. We therefore conclude that awareness, vaccine and therapy are good measure which can be used to effectively control HBV-HDV co-infection in a population. However, awareness and vaccine are better control strategies than therapy. Hence, these simulation results provide the best framework for the control of the disease; Hepatitis B virus-Hepatitis D virus (HBV-HDV) co-infection in a population.

Anahtar Kelimeler

Co-infection, Controls, Hepatitis B virus, Hepatitis D virus, Matlab, Simulation

Destekleyen Kurum

No supporting institution.

Proje Numarası

None

Teşekkür

I thank the co-authors especially Prof. G.C.E. Mbah for their immense contribution to the success of this research work.

Kaynakça

• [1] H. Fejza, S. Telaku, Prevalence of HBV and HCV among blood donors in Kosovo, Virol. J., 13, (2009), 6-21.
• [2] S. A. Kafi-abad, H. Rezvan, H. Abolghasemi, Trends in prevalence of hepatitis B virus infection among Iranian blood donors, 1998-2007. Transfus Med., 19(4), (2009), 189-94
• [3] M. Rizzetto, G. Verme, S. Recchia, Immunflorescence detection of a new antigen-antibody system (delta-antidelta) associated to hepatitis virus in the liver and serum of HBsAg carriers, Gut., 18, (1977), 996.
• [4] A. Smedile, A. Ciancio, M. Rizzetto, Hepatitis D virus. In: Richman, D.D, Whitley, R.J, Hayden, F.G, eds. Clinical virology. Washington, DC: ASM Press, (2002), 1227–1240.
• [5] S. I. Friedman, Seminars in medicine of the Beth Israel Hospital, Boston. The cellular basis of hepatic fibrosis. Mechanisms and treatment strategies, England Journal of Medicine; 328, (1993), 1828–1835.
• [6] P. Farci, Delta hepatitis: an update, J. Hepatol., 39, Suppl., 1, (2003), 212-9.
• [7] S. A. Hughes, H. Wedemeyer, P. M. Harrison, Hepatitis delta virus, Lancet, 378, (2011), 73–85.
• [8] M. Rizzetto, G. Verme, Delta hepatitis-present status, J. Hepatol., 1, (1985), 187-93.
• [9] J. M. Taylor, Hepatitis delta virus, Virology, 5; 344(1), (2006), 71-6.
• [10] S. M. Alavian, S. H. Alavian, Hepatitis D virus infection; Iran, Middle East and Central Asia, Hepatitis Monthly, 5, (2005), 137-143.
• [11] R. Esmaeili, S. M. Alavian, B. Hajibeigi, E. Sabouri, R. Edalat, A. Adeli, Phylogenetic analysis of twenty-six cases of hepatitis delta virus isolates in Tehran, Iran, Hepat Mon, 9(3), (2009), 196-200.
• [12] Z. Abbas, W. Jafri, S. Raza, Hepatitis D: Scenario in the Asia-Pacific region, World J. Gastroenterol, 7, 16(5), (2010), 554-62.
• [13] S. M. Alavian, Unthought of Problems Regarding Hepatitis D Virus Infection, Hepat Mon., 10(2), (2010), 77- 79.
• [14] R. O. Aja, D. Omale, G. C. E. Mbah, Sensitivity Analysis of the Mathematical Model on the Control of HBV-HDV co-infection Transmission Dynamics in a Given Population, Journal of the Nigerian Association of Mathematical Physics, 39, (2017), 457 - 470.
• [15] R. O. Aja, T. I. Chinebu, E. O. Eze, On the Stability of Hepatitis B Virus-Hepatitis D Virus (HBV-HDV) co-infection with Controls in a Dynamic Population, International Journal of Advances in Mathematics, 2019(2), (2019), 17-30.
• [16] H. W. Hethcote, The Mathematics of Infectious Diseases, SIAM REVIEW, 42(4), (2000), 599-653.
• [17] S. Abdulrahman, N. I. Akinwande, O. B. Awojoyogbe, U. Y. Abubakar, Sensitivity Analysis of the parameters of a Mathematical Model of Hepatitis B virus transmission, Universal Journal of Applied Mathematics, 1(4), (2013), 230-241.
• [18] I. K. Adu, A. Y. Aidoo, I. O. Darko, E. O. Frimpong, Mathematical Model of Hepatitis B in the Bosomtwe District of Ashanti Region, Ghana Applied Mathematical Sciences, 8(64), (2014), 3343 - 3358.
• [19] L. Zou, W. Zhang, Modelling the transmission dynamics and control of hepatitis B virus in China, Journal of Theoretical Biology, 10, (2009), 1-9.
• [20] A. R. Kimbir, T. Aboiyar, O. Abu, E. S. Onah, Simulation of a Mathematical Model of Hepatitis B virus Transmission Dynamics in the presence of vaccination and treatment, Mathematical Theory and Modelling, 4(12), (2014).