The Transmission Dynamics of Hepatitis B Virus Disease with Impact of Awareness and Vaccination

Abstract

Hepatitis B is a viral infection that targets the liver, caused by the Hepatitis B virus (HBV). It is one of the most common blood-borne infection, it occurs when the virus gets to the liver through the bloodstream, multiplies and releases many new viruses into the bloodstream, it inhibits the life-preserving functions of the liver, thereby increasing the risk of a serious liver disorder. Hepatitis B infection has two main stages; the acute phase and the chronic phase. In this study, we focused on these stages by developing and analyzing a new mathematical model that explains how the disease spreads within a population. We also explored different ways to control the virus, including the use of vaccines and raising awareness about infection, which can help reduce transmission and improve prevention efforts. The existence and uniqueness of the model’s solution was ascertained, using the Lipchitz condition, the boundedness of the solutions and positivity of the variables and parameters of the model were established, the later by comparison theorem. Effective basic Reproduction number of the model was obtained by next generation matrix method. The local and global stabilities of the system of equations of the model were obtained. Numerical simulations of the dynamics of the model were carried out and interpreted. It was discovered that, the importance of vaccination and Awareness of the disease (through testing), help in better management of the silent killer disease (HBV).