Two models for competition between age classes

Kostova, Tanya; Li, Jia; Friedman, Mark J.

doi:10.1016/s0025-5564(98)10077-9

Cited by 20 publications

(14 citation statements)

References 26 publications

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“…In the existing literature on propagation of diseases, various features have been identified, which govern the propagation of a given virus [4][5][6][7]16,17,22,23,26,28,30,32]. Motivated by these previous works, our model has been built so as to take into account three major features which are important in the specific case of the Puumala hantavirus -bank vole system in Europe.…”

Section: Resultsmentioning

confidence: 99%

“…Because of intraspecific competition and different behaviours between juvenile and adult individuals ( [5,17,22] and references therein), the host population is split into juvenile (J) and adult (A) subpopulations. Let J (t, x, a) and A(t, x, a) be their respective densities at time t, position x ∈ , ⊂ R n , n ≥ 1, and chronological age a ∈ (0, a † ) for juveniles and a ∈ (a 1 , a † ) for adults, with a 1 > 0 [16,26,28].…”

Section: Modellingmentioning

confidence: 99%

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A multi-structured epidemic problem with direct and indirect transmission in heterogeneous environments

Madec¹,

Wolf²

2012

Journal of Biological Dynamics

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In this work, we analyse a deterministic epidemic mathematical model motivated by the propagation of a hantavirus (Puumala hantavirus) within a bank vole population (Clethrionomys glareolus). The host population is split into juvenile and adult individuals. A heterogeneous spatial chronological age and infection age structure is considered, and also indirect transmission via the environment. Maturation rates for juvenile individuals are adult density-dependent. For the reaction-diffusion systems with age structures derived, we give global existence, uniqueness and global boundedness results. A model with transmission to humans is also studied here.

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Section: Resultsmentioning

confidence: 99%

Section: Modellingmentioning

confidence: 99%

A multi-structured epidemic problem with direct and indirect transmission in heterogeneous environments

Madec¹,

Wolf²

2012

Journal of Biological Dynamics

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“…Continuous stage structured models were proposed or studied by Nisbet and Gurney (1983), Aiello and Freedman (1990), Aiello et al (1992), Thieme (2003), de Roos et al (2003, Kuang (2004, 2005), Kostova et al (1999), Wang and Chen (1997), Wang et al (2001), Zhao (2005, 2006). Basically, modeling approaches are divided into two types according to the rate of transition: ODE approach and DDE approach.…”

Section: Modelmentioning

confidence: 99%

Dynamical Adaptation of Parental Care

et al. 2009

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Two models are proposed to simulate population growth of species with mature stage and immature stage in which there are parental cares for immature. It is assumed that the protection of mature to their immature reduces mortality of immature at the cost of reduction of reproduction. Dynamical adaptation of parental care is incorporated into the models, one of which is described with the proportional transition rate from immature to mature (ODE model) and the other one is described with a transition rate from immature to mature according to a fixed age (DDE model). For the ODE model, it is shown that the adaptation of parental care enlarges the possibility of species survival in the sense that population is permanent under the influences of the adaptation, but becomes extinct in the absence of adaptation. It is proved that the outcome of the adaptation makes the population in an optimal state. It is also observed that there are parental care switches, from noncare strategy to care strategy, as the natural death rate of immature individuals increases. The analysis of the DDE model indicates that the adaptation also enlarges the opportunity of population persistence, but the stage delay has the tendency to hinder the movement of population evolution to the optimal state. It is found that the loss rate of immature in the absence of parental care can induce different patterns to disturb the adaptation of population to optimal state. However, it is shown that the adaptation of parental care approaches to the optimal state when parental care is required for the survival of the population, for example, when the loss rate of immature or competition among mature increases or the fecundity decreases.

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“…Of course, the complexity is restricted by the Poincaré-Bendixson theory. Earlier work addressing competition between age stages [21] found that periodic orbits can surround a unique interior equilibrium. Here we show that multiple equilibria are possible, both stable and unstable periodic orbits can exist and even coexist, and homoclinic orbits can occur through the interaction of periodic orbits and multiple equilibria.…”

Section: Introductionmentioning

confidence: 99%

“…We deal with a model for one population with two stages introduced in [21] and further studied in [34,Chapter 11]. The life history of the individuals comprises a juvenile and an adult stage.…”

Section: Introductionmentioning

confidence: 99%

Multiparametric Bifurcation Analysis of a Basic Two-Stage Population Model

Baer¹,

Kooi²,

Kuznetsov³

et al. 2006

SIAM J. Appl. Math.

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In this paper we investigate long-term dynamics of the most basic model for stagestructured populations, in which the per capita transition from the juvenile into the adult class is density dependent. The model is represented by an autonomous system of two nonlinear differential equations with four parameters for a single population. We find that the interaction of intra-adult competition and intra-juvenile competition gives rise to multiple attractors, one of which can be oscillatory. A detailed numerical study reveals a rich bifurcation structure for this two-dimensional system, originating from a degenerate Bogdanov-Takens (BT) bifurcation point when one parameter is kept constant. Depending on the value of this fixed parameter, the corresponding triple critical equilibrium has either an elliptic sector or it is a topological focus, which is demonstrated by the numerical normal form analysis. It is shown that the canonical unfolding of the codimension-three BT point reveals the underlying dynamics of the model. Certain new features of this unfolding in the elliptic case, which are important in applications but have been overlooked in available theoretical studies, are established. Various three-, two-, and one-parameter bifurcation diagrams of the model are presented and interpreted in biological terms.

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Two models for competition between age classes

Cited by 20 publications

References 26 publications

A multi-structured epidemic problem with direct and indirect transmission in heterogeneous environments

A multi-structured epidemic problem with direct and indirect transmission in heterogeneous environments

Dynamical Adaptation of Parental Care

Multiparametric Bifurcation Analysis of a Basic Two-Stage Population Model

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