{"paper":{"title":"Variational characterizations of weighted eigenvalue and basic reproduction ratio for nonlocal dispersal systems and application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiazhuo Cheng, Qiru Wang, Xiandong Lin","submitted_at":"2026-03-15T07:26:39Z","abstract_excerpt":"The basic reproduction ratio is a crucial threshold parameter in infectious disease models. In nonlocal dispersal systems, its variational characterization is challenging due to the possible absence of a principal eigenvalue caused by non-compactness. In this paper, we aim to establish such a characterization even when the principal eigenvalue does not exist. To this end, we first study the spectral bound of a class of nonlocal dispersal operators, establishing a Collatz-Wielandt characterization as well as a Rayleigh-Ritz characterization when the operator is self-adjoint. Using this, we char"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.14256","kind":"arxiv","version":2},"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/2603.14256/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"}