Global dynamics of delay recruitment models with maximized lifespan

El-Morshedy, Hassan A.; Röst, Gergely; Ruiz-Herrera, Alfonso

doi:10.1007/s00033-016-0644-0

Cited by 4 publications

(3 citation statements)

References 28 publications

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“…In the context of a disease called "cyclic thrombocytopenia" [11], Bélair et al [2] found that in the case where the function g has a bell-shape given by g(x) := f 0 θ n x θ n +x n , increasing the death rate γ induces a de-stabilization of the positive equilibrium. Equation (1.1) with the same function g has also been studied by El-Morshedy et al [10] as authors identified conditions for the global stability of either the trivial equilibrium or the positive equilibrium.…”

Section: Loïs Boullu Laurent Pujo-menjouet and Jacques Bélairmentioning

confidence: 99%

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Stability analysis of an equation with two delays and application to the production of platelets

Boullu¹,

Praly²,

Bélair³

2020

Discrete &Amp; Continuous Dynamical Systems - S

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We analyze the stability of a differential equation with two delays originating from a model for a population divided into two subpopulations, immature and mature, and we apply this analysis to a model for platelet production. The dynamics of mature individuals is described by the following nonlinear differential equation with two delays: x (t) = −γx(t) + g(x(t − τ 1)) − g(x(t − τ 1 − τ 2))e −γτ 2. The method of D-decomposition is used to compute the stability regions for a given equilibrium. The centre manifold theory is used to investigate the steady-state bifurcation and the Hopf bifurcation. Similarly, analysis of the centre manifold associated with a double bifurcation is used to identify a set of parameters such that the solution is a torus in the pseudophase space. Finally, the results of the local stability analysis are used to study the impact of an increase of the death rate γ or of a decrease of the survival time τ 2 of platelets on the onset of oscillations. We show that the stability is lost through a small decrease of survival time (from 8.4 to 7 days), or through an important increase of the death rate (from 0.05 to 0.625 days −1).

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Section: Loïs Boullu Laurent Pujo-menjouet and Jacques Bélairmentioning

confidence: 99%

“…The derivation of this equation from the structured PDEs describing the two populations can be found in [10]. The immature cells are megakaryocytes, whose production rate is a decreasing function of the platelet count, and which release between 1000 and 3000 platelets after a maturation time τ 1 .…”

Section: Loïs Boullu Laurent Pujo-menjouet and Jacques Bélairmentioning

confidence: 99%

Stability analysis of an equation with two delays and application to the production of platelets

Boullu¹,

Praly²,

Bélair³

2020

Discrete &Amp; Continuous Dynamical Systems - S

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“…where ρ 1 and ρ 2 are the survival probabilities for the two different classes [14]; and a, b : [0, +∞) → (0, +∞) are continuous and bounded functions. The reader can consult [1,12,[14][15][16][17][18] for other delay differential equations with multiple delays coming from real problems. Although its importance is well recognized, seasonality is frequently neglected in mathematical models.…”

Section: Introductionmentioning

confidence: 99%

Global attractivity in tick population models incorporating seasonality and diapausing stages

El-Morshedy,

Ruiz-Herrera

2024

Proc. R. Soc. A.

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The goal of this paper is to understand the interplay between seasonality and diapause on the population dynamics of ticks. To analyse this challenge, we study a mathematical model in which the population is divided into two groups: individuals with regular development and individuals undergoing diapause. A key ingredient in the model is that the common birth and death rates depend on time in order to describe the seasonal fluctuations of the environment. From a mathematical point of view, this paper offers a novel methodology to derive criteria of global attraction. In some classical models, we give delay-dependent conditions that cover the best delay-independent criteria of global attraction. We discuss how our approach improves existing results in relevant literature. Moreover, our results are simple and versatile enough to match experimental observations. To illustrate this potential, we analyse our model with parameters coming from real observations. A message of this paper is that seasonality plays a critical role in the population dynamics of ticks.

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Criteria of global attraction in systems of delay differential equations with mixed monotonicity

El-Morshedy

Ruiz-Herrera

2020

Journal of Differential Equations

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Global dynamics of delay recruitment models with maximized lifespan

Cited by 4 publications

References 28 publications

Stability analysis of an equation with two delays and application to the production of platelets

Stability analysis of an equation with two delays and application to the production of platelets

Global attractivity in tick population models incorporating seasonality and diapausing stages

Criteria of global attraction in systems of delay differential equations with mixed monotonicity

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