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Positive Periodic Solution for Neutral-Type Integral Differential Equation Arising in Epidemic Model

Author

Listed:
  • Qing Yang

    (School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China)

  • Xiaojing Wang

    (School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China)

  • Xiwang Cheng

    (School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China)

  • Bo Du

    (School of Mathematics and Statistics, Huaiyin Normal University, Huaian 223300, China)

  • Yuxiao Zhao

    (School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China
    School of Mathematical and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China)

Abstract

This paper is devoted to investigating a class of neutral-type integral differential equations arising in an epidemic model. By using Mawhin’s continuation theorem and the properties of neutral-type operators, we obtain the existence conditions for positive periodic solutions of the considered neutral-type integral differential equation. Compared with previous results, the existence conditions in this paper are less restricted, thus extending the results of the existing literature. Finally, two examples are given to show the effectiveness and merits of the main results of this paper. Our results can be used to obtain the existence of a positive periodic solution to the corresponding non-neutral-type integral differential equation.

Suggested Citation

  • Qing Yang & Xiaojing Wang & Xiwang Cheng & Bo Du & Yuxiao Zhao, 2023. "Positive Periodic Solution for Neutral-Type Integral Differential Equation Arising in Epidemic Model," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2701-:d:1171133
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    References listed on IDEAS

    as
    1. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    2. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    3. Yong Tang & Lang Zhou & Jiahui Tang & Yue Rao & Hongguang Fan & Jihong Zhu, 2023. "Hybrid Impulsive Pinning Control for Mean Square Synchronization of Uncertain Multi-Link Complex Networks with Stochastic Characteristics and Hybrid Delays," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    4. Chunsheng Wang & Xiangdong Liu & Feng Jiao & Hong Mai & Han Chen & Runpeng Lin, 2023. "Generalized Halanay Inequalities and Relative Application to Time-Delay Dynamical Systems," Mathematics, MDPI, vol. 11(8), pages 1-11, April.
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