| Abstract | A general epidemiological model is considered, in which the host population is variable and subject to a strong Allee effect (population decline at small densities). The interaction between disease transmission, virulence and positive density-dependence due to the Allee effect can generate complex dynamics in a simple two-dimensional model of SI (susceptible - infected) type, including tri-stability, limit cycle oscillations and homoclinic loops. The various dynamical regimes can be understood mathematically in relation to a Bogdanov-Takens bifurcation. The system appears to be very sensitive to perturbations and control methods, which may have profound implications for biological conservation as well as pest management. Threshold quantities are derived that provide biological insight. The results highlight the importance of demographic processes in infectious disease models. |
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