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 language | English (US) |
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Pages (from-to) | 89-130 |
Number of pages | 42 |
Journal | Discrete and Continuous Dynamical Systems - Series B |
Volume | 19 |
Issue number | 1 |
DOIs | |
State | Published - Jan 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