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

Time-adaptive optimization in a parameter identification problem of HIV infection