Recent researches show that virus-to-cell infection and cell-to-cell
transmission are two HIV infection modes. In this paper, we propose a
delayed HIV infection model including both virus-to-cell infection and
cell-to-cell transmission and CTL immune response. The time delay
describes the phenomenon between viral entry and viral production. We
show the nonnegativity and boundedness of solution, obtain the
equilibrium points and prove local asymptotic stability of the
equilibrium points. Then the optimal control problem with antiretroviral
therapy and pharmacological delay is posed. We establish and analyze two
types of objective functions, one is linear control and the other is
quadratic control. Numerical simulations have been performed to verify
the stability of equilibrium points and show the optimal control
strategies and the effects of control on cells concentration by Matlab
and Lingo.