The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis‐)Appearance of Oscillations
Infectious diseases that affect their host on a long timescale can regulate the host population dynamics. Here we show that a strong Allee effect can lead to complex dynamics in simple epidemic models. Generally, the Allee effect renders a population bistable, but we also identify conditions for tri...
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Veröffentlicht in: | The American naturalist 2009-01, Vol.173 (1), p.72-88 |
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description | Infectious diseases that affect their host on a long timescale can regulate the host population dynamics. Here we show that a strong Allee effect can lead to complex dynamics in simple epidemic models. Generally, the Allee effect renders a population bistable, but we also identify conditions for tri‐ or monostability. Moreover, the disease can destabilize endemic equilibria and induce sustained oscillations. These disappear again for high transmissibilities, with eventually vanishing host population. Disease‐induced extinction is thus possible for density‐dependent transmission and without any alternative reservoirs. The overall complexity suggests that the system is very sensitive to perturbations and control methods, even in parameter regions with a basic reproductive ratio far beyond
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. This may have profound implications for biological conservation as well as pest management. We identify important threshold quantities and attribute the dynamical behavior to the joint interplay of a strong Allee effect and infection. |
doi_str_mv | 10.1086/593357 |
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. This may have profound implications for biological conservation as well as pest management. We identify important threshold quantities and attribute the dynamical behavior to the joint interplay of a strong Allee effect and infection.</description><identifier>ISSN: 0003-0147</identifier><identifier>EISSN: 1537-5323</identifier><identifier>DOI: 10.1086/593357</identifier><identifier>PMID: 19072071</identifier><identifier>CODEN: AMNTA4</identifier><language>eng</language><publisher>Chicago, IL: The University of Chicago Press</publisher><subject>Animal and plant ecology ; Animal, plant and microbial ecology ; Animals ; Biological and medical sciences ; Cats ; Communicable Diseases - epidemiology ; Computer Simulation ; Conservation biology ; Disease models ; Disease transmission ; Dynamical Systems ; Endemic diseases ; Epidemics ; Epidemiology ; Extinction, Biological ; Feline Acquired Immunodeficiency Syndrome - transmission ; Fundamental and applied biological sciences. Psychology ; General aspects ; Host-Pathogen Interactions ; Immunodeficiency Virus, Feline ; Infectious diseases ; Life Sciences ; Limit cycles ; Mathematics ; Models, Biological ; Oscillation ; Parasite hosts ; Pest control ; Population density ; Population Dynamics ; Population growth ; Santé publique et épidémiologie</subject><ispartof>The American naturalist, 2009-01, Vol.173 (1), p.72-88</ispartof><rights>2009 by The University of Chicago.</rights><rights>2009 INIST-CNRS</rights><rights>Copyright University of Chicago, acting through its Press Jan 2009</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c549t-16333ece1f7a9eb2636adab6eea3e458bf9fd1130f58dc4a1d17fb4d10d6b4393</citedby><cites>FETCH-LOGICAL-c549t-16333ece1f7a9eb2636adab6eea3e458bf9fd1130f58dc4a1d17fb4d10d6b4393</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,799,881,27901,27902</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21021357$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/19072071$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-00372940$$DView record in HAL$$Hfree_for_read</backlink></links><search><contributor>Donald L. DeAngelis</contributor><contributor>Matthew Keeling</contributor><creatorcontrib>Hilker, Frank M.</creatorcontrib><creatorcontrib>Langlais, Michel</creatorcontrib><creatorcontrib>Malchow, Horst</creatorcontrib><title>The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis‐)Appearance of Oscillations</title><title>The American naturalist</title><addtitle>Am Nat</addtitle><description>Infectious diseases that affect their host on a long timescale can regulate the host population dynamics. Here we show that a strong Allee effect can lead to complex dynamics in simple epidemic models. Generally, the Allee effect renders a population bistable, but we also identify conditions for tri‐ or monostability. Moreover, the disease can destabilize endemic equilibria and induce sustained oscillations. These disappear again for high transmissibilities, with eventually vanishing host population. Disease‐induced extinction is thus possible for density‐dependent transmission and without any alternative reservoirs. The overall complexity suggests that the system is very sensitive to perturbations and control methods, even in parameter regions with a basic reproductive ratio far beyond
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. This may have profound implications for biological conservation as well as pest management. We identify important threshold quantities and attribute the dynamical behavior to the joint interplay of a strong Allee effect and infection.</description><subject>Animal and plant ecology</subject><subject>Animal, plant and microbial ecology</subject><subject>Animals</subject><subject>Biological and medical sciences</subject><subject>Cats</subject><subject>Communicable Diseases - epidemiology</subject><subject>Computer Simulation</subject><subject>Conservation biology</subject><subject>Disease models</subject><subject>Disease transmission</subject><subject>Dynamical Systems</subject><subject>Endemic diseases</subject><subject>Epidemics</subject><subject>Epidemiology</subject><subject>Extinction, Biological</subject><subject>Feline Acquired Immunodeficiency Syndrome - transmission</subject><subject>Fundamental and applied biological sciences. Psychology</subject><subject>General aspects</subject><subject>Host-Pathogen Interactions</subject><subject>Immunodeficiency Virus, Feline</subject><subject>Infectious diseases</subject><subject>Life Sciences</subject><subject>Limit cycles</subject><subject>Mathematics</subject><subject>Models, Biological</subject><subject>Oscillation</subject><subject>Parasite hosts</subject><subject>Pest control</subject><subject>Population density</subject><subject>Population Dynamics</subject><subject>Population growth</subject><subject>Santé publique et épidémiologie</subject><issn>0003-0147</issn><issn>1537-5323</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqN0c1u1DAQB3ALgei2wBuAIgSolRrwxF8xt1VZaKVFvZRz5Dhj1qtsEuIEtTcegWfkSXDIqitxgZNj6-e_JzOEPAP6Fmgu3wnNmFAPyAIEU6lgGXtIFpRSllLg6ogch7CNW821eEyOQFOVUQUL0t1sMFnWNWKycg7tkJimSq6a6dO3Y0g--IAmYHifrG4H30ynzXnyeawHHwZT-toPd-d_Lg0x6TTyXz9-ni27Dk1vGotJ65LrYH1dm-lqeEIeOVMHfLpfT8iXj6ubi8t0ff3p6mK5Tq3gekhBMsbQIjhlNJaZZNJUppSIhiEXeem0qwAYdSKvLDdQgXIlr4BWsuRMsxNyNuduTF10vd-Z_q5ojS8ul-tiOou9UZnm9DtE-2a2Xd9-GzEMxc4Hi7HkBmMPCilVjNT8nxC0kFLDBF_-Bbft2Dfxh6PJpQCZi0Oa7dsQenT3dQItpqkW81QjfLFPG8sdVge2H2MEr_fABGtqN3Xeh3uXAc1gDjqd3Wg33pqvbddjCIfa5veKrnKRvvoPGtnzmW3D0PaHFymPbcgZ-w1lbszj</recordid><startdate>20090101</startdate><enddate>20090101</enddate><creator>Hilker, Frank M.</creator><creator>Langlais, Michel</creator><creator>Malchow, Horst</creator><general>The University of Chicago Press</general><general>University of Chicago Press</general><general>University of Chicago, acting through its Press</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>7QG</scope><scope>7SN</scope><scope>7SS</scope><scope>7ST</scope><scope>8FD</scope><scope>C1K</scope><scope>FR3</scope><scope>P64</scope><scope>RC3</scope><scope>SOI</scope><scope>7U6</scope><scope>7X8</scope><scope>1XC</scope></search><sort><creationdate>20090101</creationdate><title>The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis‐)Appearance of Oscillations</title><author>Hilker, Frank M. ; Langlais, Michel ; Malchow, Horst</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c549t-16333ece1f7a9eb2636adab6eea3e458bf9fd1130f58dc4a1d17fb4d10d6b4393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Animal and plant ecology</topic><topic>Animal, plant and microbial ecology</topic><topic>Animals</topic><topic>Biological and medical sciences</topic><topic>Cats</topic><topic>Communicable Diseases - epidemiology</topic><topic>Computer Simulation</topic><topic>Conservation biology</topic><topic>Disease models</topic><topic>Disease transmission</topic><topic>Dynamical Systems</topic><topic>Endemic diseases</topic><topic>Epidemics</topic><topic>Epidemiology</topic><topic>Extinction, Biological</topic><topic>Feline Acquired Immunodeficiency Syndrome - transmission</topic><topic>Fundamental and applied biological sciences. Psychology</topic><topic>General aspects</topic><topic>Host-Pathogen Interactions</topic><topic>Immunodeficiency Virus, Feline</topic><topic>Infectious diseases</topic><topic>Life Sciences</topic><topic>Limit cycles</topic><topic>Mathematics</topic><topic>Models, Biological</topic><topic>Oscillation</topic><topic>Parasite hosts</topic><topic>Pest control</topic><topic>Population density</topic><topic>Population Dynamics</topic><topic>Population growth</topic><topic>Santé publique et épidémiologie</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hilker, Frank M.</creatorcontrib><creatorcontrib>Langlais, Michel</creatorcontrib><creatorcontrib>Malchow, Horst</creatorcontrib><collection>Pascal-Francis</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Animal Behavior Abstracts</collection><collection>Ecology Abstracts</collection><collection>Entomology Abstracts (Full archive)</collection><collection>Environment Abstracts</collection><collection>Technology Research Database</collection><collection>Environmental Sciences and Pollution Management</collection><collection>Engineering Research Database</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>Genetics Abstracts</collection><collection>Environment Abstracts</collection><collection>Sustainability Science Abstracts</collection><collection>MEDLINE - Academic</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>The American naturalist</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hilker, Frank M.</au><au>Langlais, Michel</au><au>Malchow, Horst</au><au>Donald L. DeAngelis</au><au>Matthew Keeling</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis‐)Appearance of Oscillations</atitle><jtitle>The American naturalist</jtitle><addtitle>Am Nat</addtitle><date>2009-01-01</date><risdate>2009</risdate><volume>173</volume><issue>1</issue><spage>72</spage><epage>88</epage><pages>72-88</pages><issn>0003-0147</issn><eissn>1537-5323</eissn><coden>AMNTA4</coden><abstract>Infectious diseases that affect their host on a long timescale can regulate the host population dynamics. Here we show that a strong Allee effect can lead to complex dynamics in simple epidemic models. Generally, the Allee effect renders a population bistable, but we also identify conditions for tri‐ or monostability. Moreover, the disease can destabilize endemic equilibria and induce sustained oscillations. These disappear again for high transmissibilities, with eventually vanishing host population. Disease‐induced extinction is thus possible for density‐dependent transmission and without any alternative reservoirs. The overall complexity suggests that the system is very sensitive to perturbations and control methods, even in parameter regions with a basic reproductive ratio far beyond
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. This may have profound implications for biological conservation as well as pest management. We identify important threshold quantities and attribute the dynamical behavior to the joint interplay of a strong Allee effect and infection.</abstract><cop>Chicago, IL</cop><pub>The University of Chicago Press</pub><pmid>19072071</pmid><doi>10.1086/593357</doi><tpages>17</tpages></addata></record> |
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subjects | Animal and plant ecology Animal, plant and microbial ecology Animals Biological and medical sciences Cats Communicable Diseases - epidemiology Computer Simulation Conservation biology Disease models Disease transmission Dynamical Systems Endemic diseases Epidemics Epidemiology Extinction, Biological Feline Acquired Immunodeficiency Syndrome - transmission Fundamental and applied biological sciences. Psychology General aspects Host-Pathogen Interactions Immunodeficiency Virus, Feline Infectious diseases Life Sciences Limit cycles Mathematics Models, Biological Oscillation Parasite hosts Pest control Population density Population Dynamics Population growth Santé publique et épidémiologie |
title | The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis‐)Appearance of Oscillations |
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