{"paper":{"title":"A time-adaptive optimization approach for reconstructing immune response in a mathematical model of acute HIV infection using clinical data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"G. Bocharov, I. Gainova, L. Beilina","submitted_at":"2025-08-18T17:29:38Z","abstract_excerpt":"The paper proposes a time-adaptive optimization approach for determining the time-dependent immune response function in a mathematical model of acute HIV infection, using clinical data from four untreated patients. We formulate the problem as a parameter identification problem for an immune response system of ODE which includes novel component integrated into the third equation of the classical three-equation HIV model.\n  Tikhonov's regularization method, Lagrangian approach, from which we derive the optimality conditions, and a numerical scheme to solve the forward\n  and adjoint problems, as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.13123","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.13123/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}