  The paper considers a time-adaptive method for determination of drug efficacy
in a parameter identification problem (PIP) for system of ordinary differential
equations (ODE) which describe dynamics of the primary HIV infection.
Optimization approach to solve this problem is presented and a posteriori error
estimates in the Tikhonov functional and Lagrangian are formulated. Based on
these estimates a time adaptive algorithm is formulated and numerically tested
for different scenarios of noisy observations of virus population function.
Numerical results show significant improvement of reconstruction of drug
efficacy parameter when using time adaptive mesh refinement compared to usual
gradient method applied on a uniform time mesh.
