HILKER, F.M.; LANGLAIS, Michel; MALCHOW, H.

doi:10.1086/593357

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LANGLAIS, Michel
Institut de Mathématiques de Bordeaux [IMB]
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]

MALCHOW, H.

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Ce document a été publié dans

The American Naturalist. 2009-01-05, vol. 173, n° 1, p. 72-88

University of Chicago Press

Résumé en anglais

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.< Réduire

Mots clés en anglais

epidemiology

Allee effect

SI model

periodic oscillation

multistability

disease-induced extinction

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

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