ABSTRACT
The phenomenon of bifurcation in disease transmission models has been observed in a number of epidemiological models. The consequence of bifurcation is that the classical requirement of the reproduction number being less than unity becomes only a necessary, but not sufficient, for disease elimination. This paper addresses the problem of finding the causes of bifurcation in standard deterministic models for the spread of HBV diseases with non-Cytolytic cure processes on infected liver and blood cells. The model contains logistic growth of healthy liver and blood cells and non -Cytolytic cure processes of infected cells. I have got that the model exhibits back ward and forward bifurcations with some conditions. The existence of a backward bifurcation is an interesting artifact since this means that the disease cannot be eradicated by simply reducing the value of the basic reproduction number [Formula: see text] below 1.This can have important implications on drug therapy protocols, since it sheds light on possible control mechanisms for disease eradication.