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Pattern dynamics of a spatial epidemic model with time delay

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  • Song, Li-Peng
  • Zhang , Rong-Ping
  • Feng , Li-Ping
  • Shi, Qiong

Abstract

The nonlinear incidence rate can explain the complicated infectious process of disease. And time delay describing the latent period widely exists in the process of disease contagion. In this paper, a spatiotemporal epidemic model with nonlinear incidence rate is investigated. In particular, we considered that the time delay is relatively small. In this case, the characteristic equation are derived, we obtain two mechanisms of instability of the positive constant stationary state, that is, One is the diffusion induced instability, and the other one is delay induced instability. Moreover, the results of numerical simulation validate our theoretical analyses. The obtained results may well catch some major features for epidemic models.

Suggested Citation

  • Song, Li-Peng & Zhang , Rong-Ping & Feng , Li-Ping & Shi, Qiong, 2017. "Pattern dynamics of a spatial epidemic model with time delay," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 390-399.
    • Handle: RePEc:eee:apmaco:v:292:y:2017:i:c:p:390-399
    DOI: 10.1016/j.amc.2016.07.013
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    References listed on IDEAS

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    1. Li, Li, 2015. "Patch invasion in a spatial epidemic model," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 342-349.
    2. Wang, Weiming & Zhang, Lei & Wang, Hailing & Li, Zhenqing, 2010. "Pattern formation of a predator–prey system with Ivlev-type functional response," Ecological Modelling, Elsevier, vol. 221(2), pages 131-140.
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    Cited by:

    1. Wu, Zeyan & Li, Jianjuan & Liu, Shuying & Zhou, Liuting & Luo, Yang, 2019. "A spatial predator–prey system with non-renewable resources," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 381-391.
    2. Gerritse, Michiel, 2022. "COVID-19 transmission in cities," European Economic Review, Elsevier, vol. 150(C).
    3. Nian, Fuzhong & Yao, Shuanglong, 2018. "The epidemic spreading on the multi-relationships network," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 866-873.
    4. Li, Shudong & Zhao, Dawei & Wu, Xiaobo & Tian, Zhihong & Li, Aiping & Wang, Zhen, 2020. "Functional immunization of networks based on message passing," Applied Mathematics and Computation, Elsevier, vol. 366(C).

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