{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T13:16:08Z","timestamp":1780492568842,"version":"3.54.1"},"reference-count":10,"publisher":"Elsevier BV","issue":"2-3","license":[{"start":{"date-parts":[[2003,12,1]],"date-time":"2003-12-01T00:00:00Z","timestamp":1070236800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2003,12]]},"DOI":"10.1016\/s0096-3003(02)00607-0","type":"journal-article","created":{"date-parts":[[2003,2,28]],"date-time":"2003-02-28T14:00:13Z","timestamp":1046440813000},"page":"611-625","source":"Crossref","is-referenced-by-count":26,"title":["An unconditionally convergent finite-difference scheme for the SIR model"],"prefix":"10.1016","volume":"146","author":[{"given":"W.","family":"Piyawong","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.H.","family":"Twizell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.B.","family":"Gumel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/S0096-3003(02)00607-0_BIB1","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1098\/rspb.1996.0067","article-title":"Whooping cough epidemic in London, 1701\u20131812: infection dynamics seasonal forcing and the effects of malnutrition","volume":"263","author":"Duncan","year":"1996","journal-title":"Proc. R. Soc. Lond. B"},{"key":"10.1016\/S0096-3003(02)00607-0_BIB2","series-title":"Infectious Diseases of Humans: Dynamics and Control","author":"Anderson","year":"1992"},{"key":"10.1016\/S0096-3003(02)00607-0_BIB3","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1098\/rstb.1994.0158","article-title":"Modelling the different smallpox epidemics in England","volume":"346","author":"Duncan","year":"1994","journal-title":"Phil. Trans. R. Soc. Lond. B"},{"key":"10.1016\/S0096-3003(02)00607-0_BIB4","series-title":"Introduction to Dynamic Systems: Theory, Models and Applications","author":"Luenberger","year":"1979"},{"key":"10.1016\/S0096-3003(02)00607-0_BIB5","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/0025-5564(76)90132-2","article-title":"Qualitative analysis for communicable disease models","volume":"28","author":"Hethcote","year":"1976","journal-title":"Math. Biosci."},{"key":"10.1016\/S0096-3003(02)00607-0_BIB6","series-title":"Chemical Oscillations and Instability: Non-linear Chemical Kinetics","author":"Gray","year":"1994"},{"key":"10.1016\/S0096-3003(02)00607-0_BIB7","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1098\/rspa.1990.0106","article-title":"Chaos-free numerical solutions of reaction-diffusion equations","volume":"430","author":"Twizell","year":"1990","journal-title":"Proc. R. Soc. Lond. A"},{"key":"10.1016\/S0096-3003(02)00607-0_BIB8","unstructured":"W. Piyawong, Spatio-Temporal Numerical Modelling of Whooping Cough Dynamics, PhD Thesis, Brunel University, England, 2001"},{"key":"10.1016\/S0096-3003(02)00607-0_BIB9","series-title":"Numerical Methods for Ordinary Differential Systems: The Initial-Value Problem","author":"Lambert","year":"1991"},{"key":"10.1016\/S0096-3003(02)00607-0_BIB10","series-title":"Numerical Solution of Partial Differential Equations: Finite Difference Methods","author":"Smith","year":"1985"}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300302006070?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300302006070?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,27]],"date-time":"2019-03-27T08:57:27Z","timestamp":1553677047000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300302006070"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,12]]},"references-count":10,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2003,12]]}},"alternative-id":["S0096300302006070"],"URL":"https:\/\/doi.org\/10.1016\/s0096-3003(02)00607-0","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2003,12]]}}}