مشخصات پژوهش

‎It is well known that dynamical systems are very useful tools to‎ ‎study the viral disease such as HIV‎, ‎HBV‎, ‎HCV‎, ‎Ebola and‎ ‎Influenza‎. ‎This paper deals with the model‎ % ‎\begin{equation}\label{1.3}‎ ‎\begin{split}‎ ‎& \frac{dT(t)}{dt}=s-dT+rT(1-\frac{T}{T_{M}})-\frac{b_{1} TV}{1+aV}-b_{2}TI,\\‎ ‎& \frac{dI(t)}{dt}=\frac{b_{1}TV}{1+aV}+b_{2}TI-\delta I,\\‎ ‎& \frac{dV(t)}{dt}=hI-lV‎, ‎\end{split}‎ ‎\end{equation}‎ ‎which is a mathematical model of the‎ ‎cell-to-cell and the cell-free spread of HIV with both linear and‎ ‎nonlinear functional responses and logistic target cell growth‎. ‎The reproduction number of each mode of transmission has been‎ ‎calculated and their sum has been considered as the basic‎ ‎reproduction number‎. ‎Based on the values of the reproduction‎ ‎number‎, ‎the local and global stability of the rest points have‎ ‎been investigated‎. ‎Choosing a suitable bifurcation parameter‎, ‎some‎ ‎qualifications for the occurrence of Hopf bifurcation around the parameter‎ ‎have also been obtained‎. ‎Moreover‎, ‎numerical simulations are presented‎ ‎to support the analytical results‎. ‎Finally‎, ‎to study the effect of‎ ‎the drug on the disease process‎, ‎some control conditions are‎ ‎determined‎. ‎Since two modes of transmission and both linear and‎ ‎nonlinear functional responses have been included in this‎ ‎manuscript‎, ‎our obtained results are generalization of those in‎ ‎the literature‎. ‎Moreover‎, ‎the results have been obtained‎ ‎with weaker assumptions in comparison with the previous ones‎.