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

TL;DR

This paper introduces a time-adaptive optimization method for accurately identifying drug efficacy parameters in HIV infection models, demonstrating improved results over traditional methods through numerical testing.

Contribution

It presents a novel time-adaptive algorithm with a posteriori error estimates for parameter identification in HIV models, enhancing accuracy over uniform mesh approaches.

Findings

Significant improvement in parameter reconstruction accuracy.

Effective application of time adaptive mesh refinement.

Validation through numerical experiments with noisy data.

Abstract

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.