Species coexistence and periodicity in host-host-pathogen models
Models for the transmission of an infectious disease in one and two host populations with and without self-regulation are analyzed. Many unusual behaviors such as multiple positive equilibria and periodic solutions occur in previous models that use the mass-action (density-dependent) incidence. In c...
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| Veröffentlicht in: | Journal of mathematical biology 2005-12, Vol.51 (6), p.629-660 |
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| container_title | Journal of mathematical biology |
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| creator | Hethcote, Herbert W Wang, Wendi Li, Yi |
| description | Models for the transmission of an infectious disease in one and two host populations with and without self-regulation are analyzed. Many unusual behaviors such as multiple positive equilibria and periodic solutions occur in previous models that use the mass-action (density-dependent) incidence. In contrast, the models formulated using the frequency-dependent (standard) incidence have the behavior of a classic endemic model, since below the threshold, the disease dies out, and above the threshold, the disease persists and the infectious fractions approach an endemic equilibrium. The results given here reinforce previous examples in which there are major differences in behavior between models using mass-action and frequency-dependent incidences. |
| doi_str_mv | 10.1007/s00285-005-0335-5 |
| format | Article |
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Many unusual behaviors such as multiple positive equilibria and periodic solutions occur in previous models that use the mass-action (density-dependent) incidence. In contrast, the models formulated using the frequency-dependent (standard) incidence have the behavior of a classic endemic model, since below the threshold, the disease dies out, and above the threshold, the disease persists and the infectious fractions approach an endemic equilibrium. The results given here reinforce previous examples in which there are major differences in behavior between models using mass-action and frequency-dependent incidences.</description><identifier>ISSN: 0303-6812</identifier><identifier>EISSN: 1432-1416</identifier><identifier>DOI: 10.1007/s00285-005-0335-5</identifier><identifier>PMID: 15940537</identifier><language>eng</language><publisher>Germany: Springer Nature B.V</publisher><subject>Animals ; Behavior ; Coexistence ; Communicable Diseases - epidemiology ; Communicable Diseases - transmission ; Disease transmission ; Frequency dependence ; Humans ; Infectious diseases ; Logistic Models ; Mathematics ; Models, Biological ; Periodicity ; Population Dynamics ; Species Specificity</subject><ispartof>Journal of mathematical biology, 2005-12, Vol.51 (6), p.629-660</ispartof><rights>Springer-Verlag Berlin Heidelberg 2005.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c428t-601c80c1d8af9d374781e86fb8acf9b6806cfa6d06f99bcae35e2043205e093d3</citedby><cites>FETCH-LOGICAL-c428t-601c80c1d8af9d374781e86fb8acf9b6806cfa6d06f99bcae35e2043205e093d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,777,781,27905,27906</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/15940537$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Hethcote, Herbert W</creatorcontrib><creatorcontrib>Wang, Wendi</creatorcontrib><creatorcontrib>Li, Yi</creatorcontrib><title>Species coexistence and periodicity in host-host-pathogen models</title><title>Journal of mathematical biology</title><addtitle>J Math Biol</addtitle><description>Models for the transmission of an infectious disease in one and two host populations with and without self-regulation are analyzed. 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| issn | 0303-6812 1432-1416 |
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| source | MEDLINE; Springer Nature - Complete Springer Journals |
| subjects | Animals Behavior Coexistence Communicable Diseases - epidemiology Communicable Diseases - transmission Disease transmission Frequency dependence Humans Infectious diseases Logistic Models Mathematics Models, Biological Periodicity Population Dynamics Species Specificity |
| title | Species coexistence and periodicity in host-host-pathogen models |
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