The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis-)Appearance of Oscillations - Archive ouverte HAL Access content directly
Journal Articles The American Naturalist Year : 2009

The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis-)Appearance of Oscillations

F.M. Hilker
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H. Malchow
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Abstract

Infectious diseases that affect their host on a long time- scale 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 os- cillations. 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 pa- rameter regions with a basic reproductive ratio far beyond . Ro= 1. 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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hal-00372940 , version 1 (02-04-2009)

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F.M. Hilker, Michel Langlais, H. Malchow. The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis-)Appearance of Oscillations. The American Naturalist, 2009, 173 (1), pp.72-88. ⟨10.1086/593357⟩. ⟨hal-00372940⟩
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