Displaying similar documents to “Global exponential stability of positive periodic solutions for an epidemic model with saturated treatment”

Global exponential stability of almost periodic solutions for a delayed single population model with hereditary effect

Qiyuan Zhou, Jianying Shao (2015)

Annales Polonici Mathematici

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This paper is concerned with a delayed single population model with hereditary effect. Under appropriate conditions, we employ a novel argument to establish a criterion of the global exponential stability of positive almost periodic solutions of the model. Moreover, an example and its numerical simulation are given to illustrate the main result.

New results on global exponential stability of almost periodic solutions for a delayed Nicholson blowflies model

Bingwen Liu (2015)

Annales Polonici Mathematici

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This paper is concerned with a class of Nicholson's blowflies models with multiple time-varying delays, which is defined on the nonnegative function space. Under appropriate conditions, we establish some criteria to ensure that all solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give an example with numerical simulations to illustrate our main results.

Periodic Solutions in a Mathematical Model for the Treatment of Chronic Myelogenous Leukemia

A. Halanay (2012)

Mathematical Modelling of Natural Phenomena

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Existence and stability of periodic solutions are studied for a system of delay differential equations with two delays, with periodic coefficients. It models the evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding function leads to the proof of the existence of a strictly positive periodic solution by a theorem...

Some notes to existence and stability of the positive periodic solutions for a delayed nonlinear differential equations

Božena Dorociaková, Rudolf Olach (2016)

Open Mathematics

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The paper deals with the existence of positive ω-periodic solutions for a class of nonlinear delay differential equations. For example, such equations represent the model for the survival of red blood cells in an animal. The sufficient conditions for the exponential stability of positive ω-periodic solution are also considered.

Existence and uniqueness of positive periodic solutions of delayed Nicholson's blowflies models

Fei Long, Bingwen Liu (2012)

Annales Polonici Mathematici

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This paper is concerned with a class of Nicholson's blowflies models with multiple time-varying delays. By applying the coincidence degree, some criteria are established for the existence and uniqueness of positive periodic solutions of the model. Moreover, a totally new approach to proving the uniqueness of positive periodic solutions is proposed. In particular, an example is employed to illustrate the main results.

Periodic solutions to evolution equations: existence, conditional stability and admissibility of function spaces

Nguyen Thieu Huy, Ngo Quy Dang (2016)

Annales Polonici Mathematici

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We prove the existence and conditional stability of periodic solutions to semilinear evolution equations of the form u̇ = A(t)u + g(t,u(t)), where the operator-valued function t ↦ A(t) is 1-periodic, and the operator g(t,x) is 1-periodic with respect to t for each fixed x and satisfies the φ-Lipschitz condition ||g(t,x₁) - g(t,x₂)|| ≤ φ(t)||x₁-x₂|| for φ(t) being a real and positive function which belongs to an admissible function space. We then apply the results to study the existence,...

Periodic solutions of a three-species periodic reaction-diffusion system

Tiantian Qiao, Jiebao Sun, Boying Wu (2011)

Annales Polonici Mathematici

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We study a periodic reaction-diffusion system of a competitive model with Dirichlet boundary conditions. By the method of upper and lower solutions and an argument similar to that of Ahmad and Lazer, we establish the existence of periodic solutions and also investigate the stability and global attractivity of positive periodic solutions under certain conditions.