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On the Existence and Exponential Attractivity of a Unique Positive Almost Periodic Solution to an Impulsive Hematopoiesis Model with Delays

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Abstract

In this paper, a generalized model of hematopoiesis with delays and impulses is considered. By employing the contraction mapping principle and a novel type of impulsive delay inequality, we prove the existence of a unique positive almost periodic solution of the model. It is also proved that, under the proposed conditions in this paper, the unique positive almost periodic solution is globally exponentially attractive. A numerical example is given to illustrate the effectiveness of the obtained results.

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Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their constructive comments and suggestions that have helped to improve the present paper. This work was supported by the Ministry of Education and Training of Vietnam, grant B2013.17.42.

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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam

    Trinh Tuan Anh & Le Van Hien

  2. Vietnam State Council for Professor Promotion, No. 1, Dai Co Viet, Hanoi, Vietnam

    Tran Van Nhung

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  1. Trinh Tuan Anh
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  2. Tran Van Nhung
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  3. Le Van Hien
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Correspondence to Le Van Hien.

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Anh, T.T., Van Nhung, T. & Van Hien, L. On the Existence and Exponential Attractivity of a Unique Positive Almost Periodic Solution to an Impulsive Hematopoiesis Model with Delays. Acta Math Vietnam 41, 337–354 (2016). https://doi.org/10.1007/s40306-015-0149-5

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  • DOI: https://doi.org/10.1007/s40306-015-0149-5

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