Abstract:
Hepatitis B infection remains a global problem since the 1990s in Asia and
Africa and the reasons for which the hepatitis B virus disease is still in existence
remains poorly understood. Mathematical models of HBV transmission dynamics
have focused on the influence of prevention and control measures including
vaccination, antiviral treatment and linkage to care in certain regions and countries.
However, understanding the important role played by imperfect vaccination
in describing the hepatitis B virus transmission dynamics is beneficial as a
control strategy. In this study, an SV ICTR epidemiological model is proposed
to model the spread of the hepatitis B virus disease. The basic reproduction
number, R0 and the equilibria of the proposed model are discussed. It is shown
that the disease-free equilibrium point is both locally and globally asymptotically
stable when R0 < 1 while the endemic equilibrium point is proved to be
locally asymptotically stable when R0 > 1. However, when R0 = 1, the model
system shows a backward bifurcation phenomenon. Results of the numerical
simulations reveal that increasing both the vaccination and treatment rates reduces
the populations of both the acutely infected and chronic carriers which
eventually fall to zero over a given period. Hence, combining both vaccination
and treatment with the use of a vaccine with high vaccine efficacy are essential
in controlling the hepatitis B virus disease.
