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- 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 R(0) = 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.
Hilker
Frank M
FM
Center for Mathematical Biology, Mathematical and Statistical Sciences, University of Alberta, 501 CAB, Edmonton, Alberta T6G 2G1, Canada.
Langlais
Michel
M
Malchow
Horst
H
D000818:Animals; D002415:Cats; D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D053476:Extinction, Biological; D016181:Feline Acquired Immunodeficiency Syndrome / Q000635:transmission; D054884:Host-Pathogen Interactions; D016089:Immunodeficiency Virus, Feline; D008954:Models, Biological; D011157:Population Dynamics