Abstract

In this work we assume that a population's survival is dependent on the existence of a critical mass of susceptible individuals. The implications of this Allee effect is considered within the context of a Susceptible-Infectious (SI) model where infection has a negative effect on an individual's fitness: with respect to both reproduction and resource acquisition. These assumptions are built into as simple a model as possible which yields surprisingly rich dynamics. This toy model supports the possibility of multi-stability (hysteresis), saddle node and Hopf bifurcations, and catastrophic events (disease-induced extinction). The analyses provide a full picture of the system under disease-free dynamics and identifies conditions for disease persistence and disease-induced extinction. We conclude that increases in (i) the maximum birth rate of a species, (ii) the relative reproductive ability of infected individuals, or (iii) the competitive ability of a infected individuals at low density levels, or in (iv) the per-capita death rate (including disease-induced) of infected individuals, can stabilize the system (resulting in disease persistence). Conversely, increases.

Original languageEnglish (US)
Pages (from-to)89-130
Number of pages42
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume19
Issue number1
DOIs
StatePublished - Jan 1 2014

Keywords

  • Allee effects
  • Bifurcation
  • Catastrophe
  • Conservation biology
  • Infectious disease
  • Mathematical biology
  • Multiple interior equilibria
  • Reduced reproduction
  • Sustainability

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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