The Pacific Journal of Science and Technology –188– http://www.akamaiuniversity.us/PJST.htm Volume 14. Number 1. May 2013 (Spring) Mathematical Analysis of the Control of Hepatitis B Virus in a Population with Vital Dynamics. Sirajo Abdulrahman, M. Tech. 1* ; Niniuola Ifeoluwa Akinwande, Ph.D. 1 ; Omotayo Bamidele Awojoyogbe, Ph.D. 2 ; and Usman Yusuf Abubakar, Ph.D. 1 1 Department of Mathematics and Statistics, Federal University of Technology, Minna, Nigeria. 2 Department of Physics, Federal University of Technology, Minna, Nigeria. E-mail: siraja_enagi@yahoo.com * ABSTRACT In this paper, we developed and analysed a new mathematical model for the dynamics of hepatitis B virus (HBV) in a population with vital dynamics, incorporating vertical transmission, sexual maturity, the effect of public enlightenment campaign with respect to sexual behaviour, and vaccination as control measures. We obtained the effective basic reproduction number c R which can be used to control the transmission of the disease and hence, established the conditions for local and global stability of the disease free equilibrium. Bifurcation analysis was carried out using centre manifold theory which reveals a subcritical (backward) bifurcation for the model. Numerical simulations validated the analytical results and further reveals that HBV vaccination for sexually active individuals as the only control strategy can control (eliminate) the disease at even a low level of vaccination compliance. (Keywords: HBV, stability, effective basic reproduction number) INTRODUCTION Hepatitis (plural Hepatitides) is a general term that means injury to the liver characterized by the presence of inflammatory cells in the tissue of the organ (liver). Hepatitis B is a disease caused by hepatitis B virus (HBV). This disease reduces the liver’s ability to perform life-preserving functions, including filtering harmful infectious agents from the blood, storing blood sugar and converting it to usable energy forms, and producing many proteins necessary for life. Hepatitis B is fifty to one hundred times more infectious than HIV (WHO, 2009 and Adeoye, 2010). It has caused epidemics in part of Asia and Africa, and it is endemic in China (Williams, 2006). About a third of the world’s population, more than two billion peoples have been infected with hepatitis B virus (Long et al., 2008). This includes 350 million chronic carriers of the virus (Dahari et al., 2009). Transmission of hepatitis B virus results from exposure to infectious blood or body fluids containing blood. Possible forms of transmissions include (but are not limited to) unprotected sexual contact, blood transfusions, re-use of contaminated needles and syringes, and vertical transmission from mother to child during child birth. Between 90 to 95% of all babies born to infected mothers get the disease during birth. Infection with the HBV has been a major public health problem. This has two phases: Acute and Chronic. The Acute phase causes liver inflammation, vomiting, and jaundice in which the individual is infectious. Chronic hepatitis B is an infection with hepatitis B virus that last longer than six months. Once the infection becomes chronic, it may never go away completely, and may eventually cause liver cirrhosis and hepatocellular carcinoma (HCC) (Long et al., 2008 and Hoofnagle et al., 2007). HBV causes approximately 600,000 deaths each year world- wide. Moreover, 10% of people (i.e. approximately four million people world-wide) infected with HIV are co-infected with HBV (Dahari et al., 2009). In order to find an efficient way to control (prevent and treat) an infection, it is of great importance to establish its transmission dynamics. One main goal of mathematical epidemiology is to understand how to control and eradicate diseases (Ma and Ma, 2006). Mathematical models are used extensively in the study of ecological and epidemiological phenomena (Kaplan and