MATHEMATICAL MODELLING OF THE DYNAMIC OF HEPATITIS B VIRUS TRANSMISSION AND CONTROLIN PRESENCE OF VACCINATION

In this dissertation,we formulate and systematically study the global dynamics of a simple model of hepatitis B virus in termsof ordinary differential equations. This model has two important and novel features compared to the well-knownbasic virus model in the literature. Specifically, the infectious class incorporates those with one covalently closed circular DNA (cccDNA), and those with multiple cccDNA.cccDNA is the cell that restrict the treatment of Hepatitis B. As a result of this the infection reproductionnumber is no longer dependent on the patient liver size (number of initial healthy liver cells). For this model,the existence and the stability analysis of the Disease Free State is explicitly determined using the determinant and trace of the Jacobian Matrix approach. We deduce from stability analysis that the Hepatitis B virus is asymptotical stable if the < 1(Basic infection reproduction number which shows that the disease can be control using effective treatment on the infectious class and with the aid of vaccination the spread of the disease will be less compare to when vaccine is not administered.