Abstract
Despite the intervention of WHO on vaccination for reducing the spread of Hepatitis B Virus (HBV), there are records of the high prevalence of HBV in some regions. In this paper, a mathematical model was formulated to analyze the acquisition and transmission process of the virus with the view of identifying the possible way of reducing the menace and mitigating the risk of the virus. The models' positivity and boundedness were demonstrated using well-known theorems. Equating the differential equations to zero demonstrates the equilibria of the solutions i.e., the disease-free and endemic equilibrium. The next Generation Matrix method was used to compute the basic reproduction number for the models. Local and global stabilities of the models were shown via linearization and Lyapunov function methods respectively. The importance of testing and treatment on the dynamics of HBV were fully discussed in this paper. It was discovered that testing at the acute stage of the virus and chronic unaware state helps in better management of the virus.
Highlights
Hepatitis is an inflammation/scarring of the liver that contributes to various health complications, including death
Hepatitis B is most common in the Western Pacific region with prevalence rate 6.2% and Africa with prevalence rate of 6.1%, with the Americas region (0.7%) having the lowest prevalence (WHO, 2019)
The hepatitis B virus (HBV) acutely infected individuals develop to chronic without been aware if no testing at a rate, γ: The acutely infected and chronic unaware individual progress to chronic aware stage with a testing ν1,ν2 respectively and moved to treatment stage after testing at the rate δ. ω is the recovery rate of treated infected individual with full immunity
Summary
Any reports and responses or comments on the article can be found at the end of the article. Keywords : Positivity and boundedness of solutions, Equilibria of solutions, generation matrix, Linearization, Lyapunov functions, local and global stabilities
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