One way of HIV infection spreading is through the cell division of infected cells by mitosis expressed in mathematical models as a logistic process. Cell-to-cell transmission is another factor in the spread and speed of disease. In this work, we present a five-dimensional Ordinary Differential Equation model (ODE) with the logistic form for proliferation of uninfected cells, cell-to-cell and virus-to-cell transmission rate, two types of cellular and humoral immune responses, the cure rate for returning infected cells to non-infectious cells, and two treatment rates, one for reducing infectious cells and the other for blocking free viruses. We discuss the positivity and boundedness of solutions, free-equilibrium points, steady-state equilibrium points, and stability by the Routh Hurwitz criterion. The rate of reproduction is analyzed, and the useful parameters for increasing or decreasing it are identified. Numerical simulations are performed to investigate the dynamic behavior of model responses to treatment effects on disease.