{"doi":"10.1137/s0036144500371907","title":"The Mathematics of Infectious Diseases","abstract":"Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\\sigma$, and the replacement number R are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.","journal":"SIAM Review","year":2000,"id":10232,"datarank":26.740801161915755,"base_score":8.82379514872053,"endowment":8.82379514872053,"self_citation_contribution":1.3235692723080796,"citation_network_contribution":25.417231889607674,"self_endowment_contribution":1.3235692723080796,"citer_contribution":25.417231889607674,"corpus_percentile":96.5,"corpus_rank":2155,"citation_count":6793,"citer_count":198,"citers_with_citation_signal":198,"citers_with_endowment":198,"datacite_reuse_total":0,"is_dataset":false,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2000-01-01","authors":[{"id":86151,"name":"Herbert W. Hethcote","orcid":null,"position":0,"is_corresponding":true}],"reference_count":199,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-03-01T18:20:47.508186Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}