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

2019/11/29 by Larisa Beilina, Beilina, L., I. Gainova +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1912.01112

openalex publication_date 2019/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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