{"doi":"10.1016/s0025-5564(02)00108-6","title":"Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission","abstract":"A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R0<1, then the disease free equilibrium is locally asymptotically stable; whereas if R0>1, then it is unstable. Thus, R0 is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for R0 near one. This criterion, together with the definition of R0, is illustrated by treatment, multigroup, staged progression, multistrain and vector-host models and can be applied to more complex models. The results are significant for disease control.","journal":"Mathematical Biosciences","year":2002,"id":9073,"datarank":30.929431202511374,"base_score":9.18296917518005,"endowment":9.18296917518005,"self_citation_contribution":1.3774453762770078,"citation_network_contribution":29.551985826234365,"self_endowment_contribution":1.3774453762770078,"citer_contribution":29.551985826234365,"corpus_percentile":98.8,"corpus_rank":1212,"citation_count":9729,"citer_count":182,"citers_with_citation_signal":182,"citers_with_endowment":182,"datacite_reuse_total":0,"is_dataset":false,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2002-11-01","authors":[{"id":77937,"name":"James Watmough","orcid":"0000-0002-0126-0504","position":1,"is_corresponding":false},{"id":77936,"name":"P. van den Driessche","orcid":"0000-0003-1485-8326","position":0,"is_corresponding":true}],"reference_count":22,"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":[]}