2005
DOI: 10.1007/s10530-005-5215-9
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Pathogens can Slow Down or Reverse Invasion Fronts of their Hosts

Abstract: Infectious diseases are often regarded as possible explanations for the sudden collapse of biological invasions. This phenomenon is characterized by a host species, which firstly can successfully establish in a nonnative habitat, but then spontaneously disappears again. This study proposes a reaction-diffusion model consisting of a simple SI disease with vital dynamics of Allee effect type. By way of travelling wave analysis, conditions are derived under which the invasion of the host population is slowed down… Show more

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Cited by 76 publications
(65 citation statements)
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“…5A). This result draws comparison with theoretical predictions suggesting that opportunistic pathogens can slow the migration of biological species (48), and it indicates that interactions between cells can have a significant influence on population expansions.…”
Section: Resultsmentioning
confidence: 53%
“…5A). This result draws comparison with theoretical predictions suggesting that opportunistic pathogens can slow the migration of biological species (48), and it indicates that interactions between cells can have a significant influence on population expansions.…”
Section: Resultsmentioning
confidence: 53%
“…We have shown that given a fixed control quotum, pest species removal over a local area is more effective than homogeneous removal throughout the interaction arena (within the area of parameter space where bistability is observed). Partial differential equation models have been employed in biological control and predator systems previously (Lewis and van den Driessche, 1993;Ashih and Wilson, 2001;Owen and Lewis, 2001;Hilker et al, 2005). The spatial approach allows us to extend the region in parameter space over which control is possible, but also to consider applications to range expansion.…”
Section: Discussionmentioning
confidence: 99%
“…The spread of a prey population with a weak Allee effect can be slowed down in the presence of a predator (Owen and Lewis 2001). The spread of a prey population with strong Allee effect can even be reversed (Owen and Lewis 2001); see also Lewis and van den Driessche (1993) and Hilker et al (2005) for similar retreats of invasion fronts. Such spread reversals mean that the population can go extinct in the absence of any flow, thus making persistence in a stream ecosystem even more difficult.…”
Section: Allee Effectsmentioning
confidence: 99%
“…However, generally speaking, it is more difficult to find an explicit wave speed approximation in a system with Allee effect. Existing approaches include singular perturbation theory (Owen and Lewis 2001) and time scale arguments (Hilker et al 2005). Exact solutions have been found only for particular models assuming a cubic predator mortality (Petrovskii et al 2005b).…”
Section: Allee Effectsmentioning
confidence: 99%