Research article

A note on a ZIKV epidemic model with spatial structure and vector-bias

  • Received: 02 September 2021 Accepted: 08 November 2021 Published: 10 November 2021
  • MSC : 35K57, 35J57, 35B40, 92D25

  • This paper provides a supplement to a recent study of (Appl. Math. Lett. 80 (2020) 106052). We further verify that the unique endemic equilibrium is globally asymptotically stable whenever it exists.

    Citation: Yifei Pan, Siyao Zhu, Jinliang Wang. A note on a ZIKV epidemic model with spatial structure and vector-bias[J]. AIMS Mathematics, 2022, 7(2): 2255-2265. doi: 10.3934/math.2022128

    Related Papers:

  • This paper provides a supplement to a recent study of (Appl. Math. Lett. 80 (2020) 106052). We further verify that the unique endemic equilibrium is globally asymptotically stable whenever it exists.



    加载中


    [1] H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered banach spaces, SIAM Rev., 18 (1976), 620–709. doi: 10.1137/1018114.
    [2] I. I. Bogoch, O. J. Brady, M. U. Kraemer, M. German, M. I. Creatore, S. Brent, et al., Potential for Zika virus introduction and transmission in resource-limited countries in Africa and the Asia-Pacific region: a modelling study, Lancet Infect. Dis., 16 (2016), 1237–1245. doi: 10.1016/S1473-3099(16)30270-5.
    [3] B. Buonomo, C. Vargas-De-León, Stability and bifurcation analysis of a vector-bias model of malaria transmission, Math. Biosci., 242 (2013), 59–67. doi: 10.1016/j.mbs.2012.12.001.
    [4] F. Chamchod, N. F. Britton, Analysis of a vector-bias model on malaria transmission, Bull. Math. Biol., 73 (2011), 639–657. doi: 10.1007/s11538-010-9545-0.
    [5] Y. Cai, Z. Ding, B. Yang, Z. Peng, W. M. Wang, Transmission dynamics of zika virus with spatial structure-A case study in Rio de Janeiro, Brazil, Physica A, 514 (2019), 729–740. doi: 10.1016/j.physa.2018.09.100.
    [6] Y. Cai, K. Wang, W. Wang, Global transmission dynamics of a zika virus model, Appl. Math. Lett., 92 (2019), 190–195. doi: 10.1016/j.aml.2019.01.015.
    [7] L. Duan, L. huang, Threshold dynamics of a vector-host epidemic model with spatial structure and nonlinear incidence rate, Proc. Amer. Math. Soc., 149 (2021), 4789–4797. doi.org/10.1090/proc/15561.
    [8] W. E. Fitzgibbon, J. J. Morgan, G. F. Webb, An outbreak vector-host epidemic model with spatial structure: the 2015-2016 Zika outbreak in Rio De Janeiro, Theor. Biol. Med. Model., 14 (2017), 7. doi: 10.1186/s12976-017-0051-z.
    [9] D. Gao, Y. Lou, D. He, T. C. Porco, Y. Kuang, G. Chowell, et al., Prevention and control of Zika as a mosquito-borne and sexually transmitted disease: A mathematical modeling analysis, Sci. Rep., 6 (2016), 28070. doi: 10.1038/srep28070.
    [10] J. G. Kingsolver, Mosquito host choice and the epidemiology of malaria, Am. Nat., 130 (1987), 811–827. doi: 10.1086/284749.
    [11] R. Lacroix, R. Mukabana, L. C. Gouagna, J. C. Koella, Malaria infection increases attractiveness of humans to mosquitoes, PLoS Biol., 3 (2005), e298. doi: 10.1371/journal.pbio.0030298.
    [12] P. Magal, G. Webb, Y. Wu, On a vector-host epidemic model with spatial structure, Nonlinearity, 31 (2018), 5589–5614. doi: 10.1088/1361-6544/aae1e0.
    [13] P. Magal, G. Webb, Y. Wu, On the basic reproduction number of reaction-diffusion epidemic models, SIAM J. Appl. Math., 79 (2019), 284–304. doi: 10.1137/18M1182243.
    [14] K. Mischaikow, H. Smith, H. R. Thieme, Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions, Trans. Am. Math. Soc., 347 (1995), 1669–1685. doi: 10.1090/S0002-9947-1995-1290727-7.
    [15] H. L. Smith, Monotone Dynamical Systems: an Introduction to the Theory of Competitive and Cooperative Systems, Vol. 41, Providence RI, AMS, 1995.
    [16] H. R. Thieme, Convergence results and a poincaré-bendixson trichotomy for asymptotically autonomous differential equation, J. Math. Biol., 30 (1992), 755–763. doi: 10.1007/BF00173267.
    [17] H. R. Thieme, Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM J. Appl. Math., 70 (2009), 188–211. doi: 10.1137/080732870.
    [18] D. A. M. Villela, L. S. Bastos, L. M. de Carvalho, O. G. Cruz, M. F. C. Gomes, B. Durovni, et al., Zika in Rio de Janeiro: Assessment of basic reproduction number and comparison with dengue outbreaks, Epidemiol. Inf., 145 (2016), 1649–1657. doi: 10.1017/S0950268817000358.
    [19] J. Wang, Y. Chen, Threshold dynamics of a vector-borne disease model with spatial structure and vector-bias, Appl. Math. Lett., 80 (2020), 106052. doi: 10.1016/j.aml.2019.106052.
  • Reader Comments
  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1294) PDF downloads(64) Cited by(0)

Article outline

Figures and Tables

Figures(3)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog