A food chain ecoepidemic model: Infection at the bottom trophic level

Rossi, Alessandra De; Lisa, Francesco; Rubini, Luca; Zappavigna, Alberto; Venturino, Ezio

doi:10.1016/j.ecocom.2014.03.003

Cited by 14 publications

(15 citation statements)

References 28 publications

(25 reference statements)

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“…To test our detection-interpolation routine when bistability occurs, we consider the following model, describing a three level food web, with a top predator indicated by W , the intermediate population V and the bottom prey N that is affected by an epidemic. It is subdivided into the two subpopulations of susceptibles S and infected I, [10],…”

Section: D Detection-interpolation Testsmentioning

confidence: 99%

“…0.2085, Kp = 12 and Kq = 10. With this choice the equilibria E 1 = (10, 0) and E 2 = (0, 16.5) are stable, the origin E 0 is unstable and E 3 ≈ (3.8757, 3.1919) is the saddle coexistence equilibrium point partitioning the phase space domain of the system (10). The stable equilibria of ( 12) are E * 1 ≈ (1.3436, −1.2482), E * 2 ≈ (−1.3436, 1.2482) and the coexistence saddle point is E ′ 3 ≈ (0.6717, 0.4252).…”

Section: D Detection-interpolation Testsmentioning

confidence: 99%

“…We can easily verify that the origin E 0 = (0, 0), and the points associated with the survival of only one population E 1 = (K Q , 0) E 2 = (0, K P ) are equilibria of (10). To study the remaining equilibria we consider the adimensionalized system, in fact the coexistence equilibria are the roots of the eighth degree equation…”

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confidence: 99%

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Robust Approximation Algorithms for the Detection of Attraction Basins in Dynamical Systems

et al. 2015

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In dynamical systems saddle points partition the domain into basins of attractions of the remaining locally stable equilibria. This problem is rather common especially in population dynamics models. Precisely, a particular solution of a dynamical system is completely determined by its initial condition and by the parameters involved in the model. Furthermore, when the omega limit set reduces to a point, the trajectory of the solution evolves towards the steady state. But, in case of multi-stability it is possible that several steady states originate from the same parameter set. Thus, in these cases the importance of accurately reconstruct the attraction basins follows. In this paper we focus on dynamical systems of ordinary differential equations presenting three stable equilibia and we design algorithms for the detection of the points lying on the manifolds determining the basins of attraction and for the reconstruction of such manifolds. The latter are reconstructed by means of the implicit partition of unity method which makes use of radial basis functions (RBFs) as local approximants. Extensive numerical test, carried out with a Matlab package made available to the scientific community, support our findings.

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Section: D Detection-interpolation Testsmentioning

confidence: 99%

Section: D Detection-interpolation Testsmentioning

confidence: 99%

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Robust Approximation Algorithms for the Detection of Attraction Basins in Dynamical Systems

et al. 2015

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“…Campion et al investigated the effects of diseased top predators in a three‐level food web system. Rossi et al discussed the dynamics of a tri‐trophic food chain system subject to the disease affecting the bottom prey. May and Leonard studied nonlinear aspects of competition in a three‐species model system.…”

Section: Introductionmentioning

confidence: 99%

Study on autonomous and nonautonomous version of a food chain model with intraspecific competition in top predator

Roy

Alam

2019

Math Methods in App Sciences

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In this article, a three‐species food chain model with intraspecific competition in top predators has been considered. Ecological and mathematical well posedness of the model system has been established by showing that all the solutions of the model are positive and bounded. The extinction scenarios of intermediate and top predator species along with the existence and stability of all equilibrium points have been discussed. The effects of competition and conversion efficiency of top predators in the dynamics of the system have been discussed with great thrust, and it is observed that the conversion efficiency of top predators deteriorates the stability of the system, whereas intraspecific competition in top predators enhances the stable coexistence of all the populations of the system. Further, nonautonomous version of the model system has been taken into consideration to study the impact of seasonal variation in the dynamics of the model system. Sufficient conditions for the existence of a globally attractive positive periodic have been established in a periodic environment. Finally, numerical simulations have been carried out to validate our analytical findings.

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“…In [47] a simple three level food web subject to a disease affecting the bottom prey is considered. The top predators Z feed just on the intermediate population V , the bottom prey N = S + I grows logistically and is affected by a recoverable disease that is not vertically transmitted:…”

Section: Food Chainsmentioning

confidence: 99%

Ecoepidemiology: a More Comprehensive View of Population Interactions

Venturino

2015

Math. Model. Nat. Phenom.

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Abstract. Models proposed for the description of population interactions with pathogenic agents are presented. We review some basic quadratic-interactions models, then move to more complex demographics, structured models, models involving several populations, delays, plankton dynamics, the Allee effect and group behavior. In most of these cases basic reproduction numbers are evaluated and commented.

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A food chain ecoepidemic model: Infection at the bottom trophic level

Cited by 14 publications

References 28 publications

Robust Approximation Algorithms for the Detection of Attraction Basins in Dynamical Systems

Robust Approximation Algorithms for the Detection of Attraction Basins in Dynamical Systems

Study on autonomous and nonautonomous version of a food chain model with intraspecific competition in top predator

Ecoepidemiology: a More Comprehensive View of Population Interactions

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