Species decline and extinction: synergy of infectious disease and Allee effect?

Thieme, Horst R.; Dhirasakdanon, Thanate; Han, Zhun; Trevino, Roy

doi:10.1080/17513750802376313

Cited by 54 publications

(34 citation statements)

References 39 publications

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“…In a recent paper, Hilker et al [14] showed that in the presence of strong Allee effect in host demographics, a simple susceptible-infected (SI) epidemic model can exhibit stable periodic orbits (by Hopf bifurcation), multiple stationary states, and catastrophic collapses of endemic equilibria. Using a similar SI model with the strong Allee effect, Thieme et al [16] established by mathematical theorems that the transition from population decline to population collapse is mediated by a Hopf bifurcation and a heteroclinic orbit. The SI models of Hilker et al and Thieme et al are structurally similar to predator-prey models that have an Allee effect in the prey population and a linear functional response (prey eaten per predator per unit time) [2,3,6,10,[12][13][14]17,18].…”

Section: Introductionmentioning

confidence: 99%

Fatal disease and demographic Allee effect: population persistence and extinction

Friedman

Yakubu

2012

Journal of Biological Dynamics

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If a healthy stable host population at the disease-free equilibrium is subject to the Allee effect, can a small number of infected individuals with a fatal disease cause the host population to go extinct? That is, does the Allee effect matter at high densities? To answer this question, we use a susceptible-infected epidemic model to obtain model parameters that lead to host population persistence (with or without infected individuals) and to host extinction. We prove that the presence of an Allee effect in host demographics matters even at large population densities. We show that a small perturbation to the disease-free equilibrium can eventually lead to host population extinction. In addition, we prove that additional deaths due to a fatal infectious disease effectively increase the Allee threshold of the host population demographics.

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Section: Introductionmentioning

confidence: 99%

Fatal disease and demographic Allee effect: population persistence and extinction

Friedman

Yakubu

2012

Journal of Biological Dynamics

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“…In density-dependent transmission models, abrupt host extinction seems to be less general. In [57] multiple equilibria are not possible -this may be due to the assumptions that infectives do not reproduce at all or that mortality is density-independent. The model in [36] -the same as in Equations (1) and (2) but with density-dependent incidence -allows for fold catastrophes, but in a more restricted parameter range (e.g.…”

Section: Discussionmentioning

confidence: 99%

“…Numerical experiments show that the frequency-dependent model by Deredec and Courchamp [15] exhibits a saddle-node bifurcation as well (the authors did not report the possibility of multiple endemic equilibria). Furthermore, if one changes the density-dependent model by Thieme et al [57] to obey a frequency-dependent incidence, two endemic equilibria and their disappearance in a saddle-node bifurcation too become possible.…”

Section: Discussionmentioning

confidence: 99%

Population collapse to extinction: the catastrophic combination of parasitism and Allee effect

Hilker

2010

Journal of Biological Dynamics

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Infectious diseases are responsible for the extinction of a number of species. In conventional epidemic models, the transition from endemic population persistence to extirpation takes place gradually. However, if host demographics exhibits a strong Allee effect (AE) (population decline at low densities), extinction can occur abruptly in a catastrophic population crash. This might explain why species suddenly disappear even when they used to persist at high endemic population levels. Mathematically, the tipping point towards population collapse is associated with a saddle-node bifurcation. The underlying mechanism is the simultaneous population size depression and the increase of the extinction threshold due to parasite pathogenicity and Allee effect. Since highly pathogenic parasites cause their own extinction but not that of their host, there can be another saddle-node bifurcation with the re-emergence of two endemic equilibria. The implications for control interventions are discussed, suggesting that effective management may be possible for R 0 1.

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“…It receives considerable attention recently in mathematiEmail addresses: kunyasco@yahoo.com (Salisu Usaini * ), roumen.anguelov@up.ac.za (Roumen Anguelov), salisu.garba@up.ac.za (Salisu M Garba)cal models of ecology and epidemiology (for the recent works see (David et al, 2007;Friedman and Yakubu, 2012b;Hilker et al, 2007;Ling-ling and Cang, 2009;Kang and Castillo-Chavez, 2014;Sophia and Jang, 2011;Thieme et al, 2009) and the references therein). The Allee effect is a phenomenon in biology characterized by a positive relationship between population density or size and the per capita population growth rate in small populations .…”

Section: Introductionmentioning

confidence: 99%

Dynamics of SI epidemic with a demographic Allee effect

Usaini

Anguelov

Garba

2015

Theoretical Population Biology

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In this paper, we present an extended SI model of Hilker et al. (2009). In the presented model the birth rate and the death rate are both modeled as quadratic polynomials. This approach provides ample opportunity for taking into account the major contributors to an Allee effect and effectively captures species' differential susceptibility to the Allee effects. It is shown that, the behaviors (persistence or extinction) of the model solutions are characterized by the two essential threshold parameters λ 0 and λ 1 of the transmissibility λ and a threshold quantity µ * of the disease pathogenicity µ. If λ < λ 0 , the model is bistable and a disease cannot invade from arbitrarily small introductions into the host population at the carrying capacity, while it persists when λ > λ 0 and µ < µ * . When λ > λ 1 and µ > µ * , the disease derives the host population to extinction with origin as the only global attractor. For the special cases of the model, verifiable conditions for host population persistence (with or without infected individuals) and host extinction are derived. Interestingly, we show that if the values of the parameters α and β of the extended model are restricted, then the two models are similar. Numerical simulations show how the parameter β affects the dynamics of the model with respect to the host population persistence and extinction.

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Species decline and extinction: synergy of infectious disease and Allee effect?

Cited by 54 publications

References 39 publications

Fatal disease and demographic Allee effect: population persistence and extinction

Fatal disease and demographic Allee effect: population persistence and extinction

Population collapse to extinction: the catastrophic combination of parasitism and Allee effect

Dynamics of SI epidemic with a demographic Allee effect

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