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Oscillation of the Impulsive Hematopoiesis Model with Positive and Negative Coefficients


  • Iman Sabeeh Hadeed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
  • Hussain Ali Mohamad Department of Mathematics, College of Science for Woman, University of Baghdad, Baghdad, Iraq.



Delay differential equations, Hematopoiesis model, Impulsive, Oscillation, Sufficient conditions.



In this paper, the problem of oscillating solutions for an impulsive hematopoiesis model with positive and negative coefficients is investigated. There are several evolutionary processes, which frequently encounter dramatic shifts at specific times and are sensitive to short-term perturbations. As a result, we construct several oscillation criteria that are either brand-new or enhance many of recent findings in the literature. We also give illustrations of how impulsiveness affects the oscillating solutions of the hematopoiesis model.


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Ma S. Bifurcation Analysis of Periodic Oscillation in a Hematopoietic Stem Cells Model with Time Delay Control. Math Probl Eng. 2022 May 25; 2022.

Mohamad HA, Jassim EJ. The oscillation of lasota-wazewska model with a variable probability of death of red blood cell. J Phys Conf Ser. 2021 Jul 1; 1963(1): 012158.

Zhan N, Wu A. Potential Effects of Delay on the Stability of a Class of Impulsive Neural Networks. Complexity. 2022 Jul 15; 2022.

Iman SH, Mohamad HA. Oscillation of the Solutions for Hematopoiesis Models. Iraqi J Sci. 2022 Oct 30; 64)10(: 5165-5172.

Sharba BA, Jaddoa AF. On the Existence and Oscillatory Solutions of Multiple Delay Differential Equation. Iraqi J Sci. 2023 Feb 28; 64(2): 878-92.

Jaddoa AF. Oscillation and Asymptotic Behavior of First and Second Order Impulsive Neutral Differential Equations. PhD[dissertation]. A Thesis Submitted to the College of Science, Baghdad, University of Baghdad;2019.

Ravi P, Agarwal R, Karakoc F, Zafer A. A survey on oscillation of impulsive ordinary differential equations. Adv Differ Equ. 2010 Dec; 2010: 1-52.

Nieto JJ. Solution of a fractional logistic ordinary differential equation. Appl Math Lett. 2022 Jan 1; 123: 107568.

Manzanas Lopez D, Musau P, Hamilton NP, Johnson TT. Reachability analysis of a general class of neural ordinary differential equations. Lect Notes Comput. Sci. Cham: Springer IPP. 2022 Aug 29; 13465: 258–77.

Bouakkaz A. Positive periodic solutions for a class of first-order iterative differential equations with an application to a hematopoiesis model Carpathian J Math. 2022 Jan 1; 38(2): 347-55.

Mohsen AA, Naji RK. Stability and Bifurcation of a Delay Cancer Model in the Polluted Environment. Adv Syst Sci Appl. 2022 Sep 30; 22(3): 7-1.

Heidarkhani S, Ferrara M, Caristi G, Salari A. Existence of three solutions for impulsive nonlinear fractional boundary value problems. Opusc Math. 2017; 37(2): 281-301.

Attia ER, Chatzarakis GE. Oscillation tests for difference equations with non-monotone retarded arguments Dyn Contin Discrete Impuls Syst ser A Math Anal. 2022 Jan 1; 123: 107551.

Mohamad HA, Jaddoa AF. Oscillation Criteria for Solutions of Neutral Differential Equations of Impulses Effect with Positive and Negative Coefficients. Baghdad Sci J. 2020 Apr 1; 17(2): 537-44.

Monje ZA, Ahmed BA. A study of stability of first-order delay differential equations using fixed point theorem Banach. Iraqi J Sci. 2019 Dec 29; 60(12): 2719-24.

Wen K, Zeng Y, Peng H, Huang L. Philos-type oscillation criteria for second-order linear impulsive differential equation with damping. Bound Value Probl. 2019 Dec; 2019:1-6.

Agarwal RP, Karakoç F. A survey on oscillation of impulsive delay differential equations. Comput Math Appl. 2010 Sep 1; 60(6): 1648-85.

Faria T, Oliveira JJ. Global asymptotic stability for a periodic delay hematopoiesis model with impulses. Appl Math Model. 2020 Mar 1; 79: 843-64.

Vanhie JJ., De Lisio M. How does lifestyle affect Hematopoiesis and the marrow microenvironment? Toxicologic Pathology. 2022; 50(7): 858-866.

King KY, Goodell MA. Inflammatory modulation of HSCs: viewing the HSC as a foundation for the immune response. Nat Rev Immunol. 2011 Oct; 11(10): 685-92.