Codimension-one bifurcation and stability analysis in an immunosuppressive infection model

One of the important medical problems is infectious diseases such as HIV and hepatitis which annually causes the death of many people. So it is important to study infectious diseases parametric models. In this paper, we investigate differential equations system of HIV and hepatitis (with delay and without delay) from the stability and codimension-one bifurcation point of view. We show that their dynamical behaviour will change when the parameters vary. We prove that this model has a saddle-node bifurcation and transcritical bifurcation when the delay parameter is absent. Also by using the center manifold theory, we show that the delay model has a saddle-node bifurcation.