{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:7NXNKDSOTGFSI5PQ4ZTJDFGEFL","short_pith_number":"pith:7NXNKDSO","schema_version":"1.0","canonical_sha256":"fb6ed50e4e998b2475f0e6669194c42ae7f813ca964b83a625e78995d0f0da87","source":{"kind":"arxiv","id":"1902.09307","version":1},"attestation_state":"computed","paper":{"title":"Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dang H. Nguyen, Ky Tran, N. T. Dieu, T. D. Tuong","submitted_at":"2019-02-25T14:47:56Z","abstract_excerpt":"In this paper, we consider a stochastic SIRS model with general incidence rate and perturbed by both white noise and color noise. We determine the threshold $\\lambda$ that is used to classify the extinction and permanence of the disease. In particular, $\\lambda<0$ implies that the disease-free $(K, 0, 0)$ is globally asymptotic stable, i.e., the disease will eventually disappear. If $\\lambda>0$ the epidemic is strongly stochastically permanent. Our result is considered as a significant generalization and improvement over the results in \\cite{HZ1, GLM1, LOK1, SLJJ1, ZJ1}."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1902.09307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-25T14:47:56Z","cross_cats_sorted":[],"title_canon_sha256":"b404034173d9fbf6e578743bebdf41ec9e783c7b77c7626b0bfcd1f870174068","abstract_canon_sha256":"3e91fc3a577a5f2aff4fafaaf0ada7c5cdb92b0577023bc31d9fcbbcdc2ed73d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:46.091158Z","signature_b64":"VDtjwdQdAESQmys2OFCN841kW/5YtqLhHUT+Cx7fyXeUVFNW2K02RuJ6S/giYfVFw9hi0LaAhi9vhw0GMRMKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb6ed50e4e998b2475f0e6669194c42ae7f813ca964b83a625e78995d0f0da87","last_reissued_at":"2026-05-17T23:52:46.090543Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:46.090543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extinction and permanence in a stochastic SIRS model in regime-switching with general incidence rate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dang H. Nguyen, Ky Tran, N. T. Dieu, T. D. Tuong","submitted_at":"2019-02-25T14:47:56Z","abstract_excerpt":"In this paper, we consider a stochastic SIRS model with general incidence rate and perturbed by both white noise and color noise. We determine the threshold $\\lambda$ that is used to classify the extinction and permanence of the disease. In particular, $\\lambda<0$ implies that the disease-free $(K, 0, 0)$ is globally asymptotic stable, i.e., the disease will eventually disappear. If $\\lambda>0$ the epidemic is strongly stochastically permanent. Our result is considered as a significant generalization and improvement over the results in \\cite{HZ1, GLM1, LOK1, SLJJ1, ZJ1}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09307","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.09307","created_at":"2026-05-17T23:52:46.090635+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.09307v1","created_at":"2026-05-17T23:52:46.090635+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09307","created_at":"2026-05-17T23:52:46.090635+00:00"},{"alias_kind":"pith_short_12","alias_value":"7NXNKDSOTGFS","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"7NXNKDSOTGFSI5PQ","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"7NXNKDSO","created_at":"2026-05-18T12:33:12.712433+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7NXNKDSOTGFSI5PQ4ZTJDFGEFL","json":"https://pith.science/pith/7NXNKDSOTGFSI5PQ4ZTJDFGEFL.json","graph_json":"https://pith.science/api/pith-number/7NXNKDSOTGFSI5PQ4ZTJDFGEFL/graph.json","events_json":"https://pith.science/api/pith-number/7NXNKDSOTGFSI5PQ4ZTJDFGEFL/events.json","paper":"https://pith.science/paper/7NXNKDSO"},"agent_actions":{"view_html":"https://pith.science/pith/7NXNKDSOTGFSI5PQ4ZTJDFGEFL","download_json":"https://pith.science/pith/7NXNKDSOTGFSI5PQ4ZTJDFGEFL.json","view_paper":"https://pith.science/paper/7NXNKDSO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.09307&json=true","fetch_graph":"https://pith.science/api/pith-number/7NXNKDSOTGFSI5PQ4ZTJDFGEFL/graph.json","fetch_events":"https://pith.science/api/pith-number/7NXNKDSOTGFSI5PQ4ZTJDFGEFL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7NXNKDSOTGFSI5PQ4ZTJDFGEFL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7NXNKDSOTGFSI5PQ4ZTJDFGEFL/action/storage_attestation","attest_author":"https://pith.science/pith/7NXNKDSOTGFSI5PQ4ZTJDFGEFL/action/author_attestation","sign_citation":"https://pith.science/pith/7NXNKDSOTGFSI5PQ4ZTJDFGEFL/action/citation_signature","submit_replication":"https://pith.science/pith/7NXNKDSOTGFSI5PQ4ZTJDFGEFL/action/replication_record"}},"created_at":"2026-05-17T23:52:46.090635+00:00","updated_at":"2026-05-17T23:52:46.090635+00:00"}