Seasonality and period-doubling bifurcations in an epidemic model
The annual incidence rates of some endemic infectious diseases are steady while others fluctuate dramatically, often in a regular cycle. In order to investigate the role of seasonality in driving cycles of recurrent epidemics, we analyze numerically the susceptible/exposed/infective/recovered (SEIR)...
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| Veröffentlicht in: | Journal of theoretical biology 1984-10, Vol.110 (4), p.665-679 |
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| container_end_page | 679 |
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| container_title | Journal of theoretical biology |
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| creator | Aron, Joan L. Schwartz, Ira B. |
| description | The annual incidence rates of some endemic infectious diseases are steady while others fluctuate dramatically, often in a regular cycle. In order to investigate the role of seasonality in driving cycles of recurrent epidemics, we analyze numerically the susceptible/exposed/infective/recovered (SEIR) epidemic model with seasonal transmission. We show that small-amplitude periodic solutions exhibit a sequence of period-doubling bifurcations as the amplitude of seasonal variation increases, predicting a transition to chaos of the kind studied in other biological contexts. The epidemiological implication is that the seasonal mechanism generating biennial epidemics may not be able to account for small-amplitude recurrent epidemics of arbitrary periodicity. |
| doi_str_mv | 10.1016/S0022-5193(84)80150-2 |
| format | Article |
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In order to investigate the role of seasonality in driving cycles of recurrent epidemics, we analyze numerically the susceptible/exposed/infective/recovered (SEIR) epidemic model with seasonal transmission. We show that small-amplitude periodic solutions exhibit a sequence of period-doubling bifurcations as the amplitude of seasonal variation increases, predicting a transition to chaos of the kind studied in other biological contexts. 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In order to investigate the role of seasonality in driving cycles of recurrent epidemics, we analyze numerically the susceptible/exposed/infective/recovered (SEIR) epidemic model with seasonal transmission. We show that small-amplitude periodic solutions exhibit a sequence of period-doubling bifurcations as the amplitude of seasonal variation increases, predicting a transition to chaos of the kind studied in other biological contexts. The epidemiological implication is that the seasonal mechanism generating biennial epidemics may not be able to account for small-amplitude recurrent epidemics of arbitrary periodicity.</description><subject>Biological and medical sciences</subject><subject>Communicable Diseases - epidemiology</subject><subject>Disease Outbreaks - epidemiology</subject><subject>England</subject><subject>Epidemiology. Vaccinations</subject><subject>General aspects</subject><subject>Humans</subject><subject>Infectious diseases</subject><subject>Mathematics</subject><subject>Measles - epidemiology</subject><subject>Medical sciences</subject><subject>Models, Biological</subject><subject>New York City</subject><subject>Periodicity</subject><subject>Seasons</subject><subject>Time Factors</subject><subject>Wales</subject><issn>0022-5193</issn><issn>1095-8541</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1984</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqFkE1LxDAQhoMoun78BKEHET1UJ03SJCcR8QsED-o5pMlUIm2zJq3gv7e6y149zeF93pnhIeSYwgUFWl--AFRVKahmZ4qfK6ACymqLLChoUSrB6TZZbJA9sp_zBwBozupdsluLinJVL8j1C9ocB9uF8buwgy-WmEL0pY9T04XhvWhCOyVnxxCHXIRhZgpcBo99cEUfPXaHZKe1Xcaj9Twgb3e3rzcP5dPz_ePN9VPpBMixdIBSaW-BSccbbK2qpfPKN8hkJVhdaaYr6ZltG4eaKs8159JbBg6sQmAH5HS1d5ni54R5NH3IDrvODhinbKRQogYQMyhWoEsx54StWabQ2_RtKJhfdeZPnfn1YhQ3f-pMNfeO1wempke_aa1dzfnJOrfZ2a5NdnAhbzANjFMpZ-xqheEs4ytgMtkFHBz6kNCNxsfwzyM_q4yKaA</recordid><startdate>19841021</startdate><enddate>19841021</enddate><creator>Aron, Joan L.</creator><creator>Schwartz, Ira B.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope></search><sort><creationdate>19841021</creationdate><title>Seasonality and period-doubling bifurcations in an epidemic model</title><author>Aron, Joan L. ; Schwartz, Ira B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c507t-c0e789da037c4befa867cd8dbe372536293927d3afbce918d49447da30c0a8e03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1984</creationdate><topic>Biological and medical sciences</topic><topic>Communicable Diseases - epidemiology</topic><topic>Disease Outbreaks - epidemiology</topic><topic>England</topic><topic>Epidemiology. 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| ispartof | Journal of theoretical biology, 1984-10, Vol.110 (4), p.665-679 |
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| language | eng |
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| source | MEDLINE; Elsevier ScienceDirect Journals Complete |
| subjects | Biological and medical sciences Communicable Diseases - epidemiology Disease Outbreaks - epidemiology England Epidemiology. Vaccinations General aspects Humans Infectious diseases Mathematics Measles - epidemiology Medical sciences Models, Biological New York City Periodicity Seasons Time Factors Wales |
| title | Seasonality and period-doubling bifurcations in an epidemic model |
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