{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NP6QHBHLC7WIDL63H6P3ADXCKK","short_pith_number":"pith:NP6QHBHL","schema_version":"1.0","canonical_sha256":"6bfd0384eb17ec81afdb3f9fb00ee2528817df608611a302d0ddeaa180580eb2","source":{"kind":"arxiv","id":"2605.12773","version":1},"attestation_state":"computed","paper":{"title":"The interplay of network structure and correlated infectious traits in epidemic models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A framework with joint distributions of susceptibility and transmissibility across network subgroups yields analytical expressions for the basic reproduction number in SIR models.","cross_cats":["physics.soc-ph"],"primary_cat":"q-bio.PE","authors_text":"Abhay Gupta, Nicholas W. Landry","submitted_at":"2026-05-12T21:35:43Z","abstract_excerpt":"Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and infection rates is well-understood, less studied is the impact of population-level covariance between susceptibility and transmissibility, despite empirical evidence showing that both susceptibility and transmission vary across individuals. We introduce a mathematical modeling framework incorporating population subgroups, each with its own joint distribution of"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.12773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2026-05-12T21:35:43Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"06c913d7585685c8883d8a5f737e869e899eb152be6800fadaa82c9bc67fd5a3","abstract_canon_sha256":"5a1ca2b498c9ac534e2970c31bf65f89013d6432771201f6e5e5b05cce71ac6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:20.072135Z","signature_b64":"VJ4NEEZpzFCtNXwBfyg0fO60JPcGERdf3gdMwBTffeQjj70RCuj0wJlXATljkZWVp07btHxVQ3V2xO9RSVhuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bfd0384eb17ec81afdb3f9fb00ee2528817df608611a302d0ddeaa180580eb2","last_reissued_at":"2026-05-18T03:09:20.071379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:20.071379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The interplay of network structure and correlated infectious traits in epidemic models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A framework with joint distributions of susceptibility and transmissibility across network subgroups yields analytical expressions for the basic reproduction number in SIR models.","cross_cats":["physics.soc-ph"],"primary_cat":"q-bio.PE","authors_text":"Abhay Gupta, Nicholas W. Landry","submitted_at":"2026-05-12T21:35:43Z","abstract_excerpt":"Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and infection rates is well-understood, less studied is the impact of population-level covariance between susceptibility and transmissibility, despite empirical evidence showing that both susceptibility and transmission vary across individuals. We introduce a mathematical modeling framework incorporating population subgroups, each with its own joint distribution of"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We derive analytical expressions for the basic reproduction number, which, when reduced, corroborates prior results and validate these results with numerical simulations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The framework assumes that population subgroups can be defined with independent joint distributions of susceptibility and transmissibility that interact with network structure in a way that permits closed-form reproduction-number expressions; this may not hold if real correlations between traits and network position are more complex or data-driven.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new modeling framework for SIR epidemics incorporates joint distributions of susceptibility and transmissibility across network subgroups, producing analytical basic reproduction numbers that reduce to known results and are validated by simulations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A framework with joint distributions of susceptibility and transmissibility across network subgroups yields analytical expressions for the basic reproduction number in SIR models.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"820229a59e5d623329ae4e99fad0da4613c7fca589ba6818723e9134c214d2bf"},"source":{"id":"2605.12773","kind":"arxiv","version":1},"verdict":{"id":"a18df7e9-84f7-421f-b855-b3a11be0146f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:36:40.965984Z","strongest_claim":"We derive analytical expressions for the basic reproduction number, which, when reduced, corroborates prior results and validate these results with numerical simulations.","one_line_summary":"A new modeling framework for SIR epidemics incorporates joint distributions of susceptibility and transmissibility across network subgroups, producing analytical basic reproduction numbers that reduce to known results and are validated by simulations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The framework assumes that population subgroups can be defined with independent joint distributions of susceptibility and transmissibility that interact with network structure in a way that permits closed-form reproduction-number expressions; this may not hold if real correlations between traits and network position are more complex or data-driven.","pith_extraction_headline":"A framework with joint distributions of susceptibility and transmissibility across network subgroups yields analytical expressions for the basic reproduction number in SIR models."},"references":{"count":52,"sample":[{"doi":"","year":null,"title":"In the following, we analytically derive the eigenval- ues ofJfor several common network models to obtain an analytical expression forR 0. B. Random mixing Here, we assume a single subpopulation, i.e.","work_id":"2e897e7e-9926-401a-81b7-1c3ee408a013","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"In this case, N(g 1) =N(g 2) =N/2, P(g 1 |g 1) =P(g 2 |g 2) =p in, P(g 1 |g 2) =P(g 2 |g 1) =p out","work_id":"72d79db3-90a9-4f69-8a28-6533302ef0cd","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"We specify that N(g 1) =rN, andN(g 2) = (1−r)N(whereris the fraction of individuals in community 1)","work_id":"847c26f0-4da0-456c-8d66-1f352c3ce640","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Then, individual 8 values ofδandεwere sampled from this distribution, with different Σ values for each community","work_id":"6f3cffba-d0ce-4b3b-9b85-4c44f0485e36","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1927,"title":"W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Chara","work_id":"46aea73a-71de-4eb2-9be9-673758cbc0f0","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":52,"snapshot_sha256":"0dae33d116744a19e1b52bdd30dfc7f0b37d626fcdd43ed7b16a09779d7990fe","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"8caaee033905ec78c0bbc3245f4e3a46c8605246c3a15a57f23e8b59fe8a4859"},"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":"2605.12773","created_at":"2026-05-18T03:09:20.071509+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.12773v1","created_at":"2026-05-18T03:09:20.071509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.12773","created_at":"2026-05-18T03:09:20.071509+00:00"},{"alias_kind":"pith_short_12","alias_value":"NP6QHBHLC7WI","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"NP6QHBHLC7WIDL63","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"NP6QHBHL","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":1,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NP6QHBHLC7WIDL63H6P3ADXCKK","json":"https://pith.science/pith/NP6QHBHLC7WIDL63H6P3ADXCKK.json","graph_json":"https://pith.science/api/pith-number/NP6QHBHLC7WIDL63H6P3ADXCKK/graph.json","events_json":"https://pith.science/api/pith-number/NP6QHBHLC7WIDL63H6P3ADXCKK/events.json","paper":"https://pith.science/paper/NP6QHBHL"},"agent_actions":{"view_html":"https://pith.science/pith/NP6QHBHLC7WIDL63H6P3ADXCKK","download_json":"https://pith.science/pith/NP6QHBHLC7WIDL63H6P3ADXCKK.json","view_paper":"https://pith.science/paper/NP6QHBHL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.12773&json=true","fetch_graph":"https://pith.science/api/pith-number/NP6QHBHLC7WIDL63H6P3ADXCKK/graph.json","fetch_events":"https://pith.science/api/pith-number/NP6QHBHLC7WIDL63H6P3ADXCKK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NP6QHBHLC7WIDL63H6P3ADXCKK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NP6QHBHLC7WIDL63H6P3ADXCKK/action/storage_attestation","attest_author":"https://pith.science/pith/NP6QHBHLC7WIDL63H6P3ADXCKK/action/author_attestation","sign_citation":"https://pith.science/pith/NP6QHBHLC7WIDL63H6P3ADXCKK/action/citation_signature","submit_replication":"https://pith.science/pith/NP6QHBHLC7WIDL63H6P3ADXCKK/action/replication_record"}},"created_at":"2026-05-18T03:09:20.071509+00:00","updated_at":"2026-05-18T03:09:20.071509+00:00"}