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
Hauptverfasser: Hilker, Frank M., Langlais, Michel, Malchow, Horst
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Langlais, Michel
Malchow, Horst
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 \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $R_{0}=1$ \end{document} . 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.
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DeAngelis ; Matthew Keeling</contributor><creatorcontrib>Hilker, Frank M. ; Langlais, Michel ; Malchow, Horst ; Donald L. DeAngelis ; Matthew Keeling</creatorcontrib><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. 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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. 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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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source Jstor Complete Legacy; MEDLINE; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals
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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