Dynamics of a stage-structured single population model with state-dependent delay

Wang, Yan; Liu, Xianning; Wei, Yangjiang

doi:10.1186/s13662-018-1824-3

Cited by 9 publications

(11 citation statements)

References 31 publications

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“…DDMs are therefore typically continuous models [6]. Thinking in population rather than single individual terms, we have from age-structured to stage-structured models [18][19][20]. Stage-structured models are particularly helpful in entomology, as population dynamics of insects involve different life stages with different growth rates, responses to external stimuli, and so on.…”

Section: Pest Population Growth and Dynamicmentioning

confidence: 99%

Models Applied to Grapevine Pests: A Review

Lessio

Alma

2021

Insects

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This paper reviews the existing predictive models concerning insects and mites harmful to grapevine. A brief conceptual description is given on the definition of a model and about different types of models: deterministic vs. stochastics, continuous vs. discrete, analytical vs. computer-based, and descriptive vs. data-driven. The main biological aspects of grapevine pests covered by different types of models are phenology, population growth and dynamics, species distribution, and invasion risk. A particular emphasis is put on forecasting epidemics of plant disease agents transmitted by insects with sucking-piercing mouthparts. The most investigated species or groups are the glassy-winged sharpshooter Homalodisca vitripennis (Germar) and other vectors of Xylella fastidiosa subsp. fastidiosa, a bacterium agent of Pierce’s disease; the European grape berry moth, Lobesia botrana (Denis and Schiffermuller); and the leafhopper Scaphoideus titanus Ball, the main vector of phytoplasmas agents of Flavescence dorée. Finally, the present and future of decision-support systems (DSS) in viticulture is discussed.

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Section: Pest Population Growth and Dynamicmentioning

confidence: 99%

Models Applied to Grapevine Pests: A Review

Lessio

Alma

2021

Insects

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“…Motivated by the ideas in [6,8,13,26], we consider the growth of predator through immature and mature two stages. In order to distinguish immature individuals, y j (t), from mature ones, y(t), we introduce a threshold age τ(y(t)), which is the maturation time for an immature individual that matures at time t depending on the number of mature predator, y(t).…”

Section: Model Derivationmentioning

confidence: 99%

“…For the global dynamics of the system, they discuss an attracting region which is determined by solutions, and the region collapses to the interior equilibrium in the constant delay case. In 2018, Wang et al [26] established and analyzed a state-dependent time-delay model with the delayed time-derivative term:…”

Section: Introductionmentioning

confidence: 99%

“…This model is clearly different from the previous models in the sense that it includes the correction term 1 − τ ′ (z(t))z ′ (t) in the maturity rate. Permanence of the system was analyzed, and explicit bounds for the eventual behaviors of the immature and mature populations are established in [26], while the global stability was not discussed. In this paper, following the research method of Wang et al [26], based on the age structure model, we consider a SDTD predator-prey model where the predators was divided into immature and mature, mature delay is a monotonically increasing continuous differentiable bounded function that depends on the number of adult predators.…”

Section: Introductionmentioning

confidence: 99%

“…Permanence of the system was analyzed, and explicit bounds for the eventual behaviors of the immature and mature populations are established in [26], while the global stability was not discussed. In this paper, following the research method of Wang et al [26], based on the age structure model, we consider a SDTD predator-prey model where the predators was divided into immature and mature, mature delay is a monotonically increasing continuous differentiable bounded function that depends on the number of adult predators. In other words, if the number of adult predators is large, the maturity period is longer, and the population size is reduced as slow growth of adult predators.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global Dynamics of a Predator-Prey Model with State-Dependent Maturation-Delay

Zhang¹,

Yuan²,

Lv³

et al. 2021

Preprint

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In this paper, a stage structured predator-prey model with general nonlinear type of functional response is established and analyzed. The state-dependent time delay (hereafter SDTD) is the time taken from predator's birth to its maturity, formatted as a monotonical (ly) increasing, continuous(ly) differentiable and bounded function on the number of mature predator. The model is quite different from many previous models with SDTD, in the sense that the derivative of delay on the time is involved in the model. First, we have shown that for a large class of commonly used types of functional responses, including Holling types I, II and III, Beddington-DeAngelistype (hereafter BD-type), etc, the predator coexists with the prey permanently if and only if the predator's net reproduction number is larger than one unit; Secondly, we have discussed the local stability of the equilibria of the model; Finally, for the special case of BD-type functional response, we claim that if the system is permanent, that is, the derivative of SDTD on the state is small enough and the predator interference is large enough, then the coexistence equilibrium is globally asymptotically stable.

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Null controllability of a retarded population dynamics model with interior degeneracy

Diao

Echarroudi

Khalil

2023

Math Methods in App Sciences

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In this work, we establish a null controllability property of a dispersive age‐structured population dynamics model with finite‐time delay on the mortality rate term. We assume that the dispersion term includes an interior degeneracy satisfying some suitable assumptions. To achieve our main results, we act according to the classical procedure, which is the Carleman estimates of a suitable adjoint system, and then its associated observability inequality. It is well known that the basis of Carleman's estimates is an adjusted weight function and one of the originalities of our article is the expression of the function as a function of age and time variables.

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Dynamics of a stage-structured single population model with state-dependent delay

Cited by 9 publications

References 31 publications

Models Applied to Grapevine Pests: A Review

Models Applied to Grapevine Pests: A Review

Global Dynamics of a Predator-Prey Model with State-Dependent Maturation-Delay

Null controllability of a retarded population dynamics model with interior degeneracy

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