Research article

A note on advection-diffusion cholera model with bacterial hyperinfectivity

  • Received: 15 August 2020 Accepted: 18 October 2020 Published: 28 October 2020
  • This note gives a supplement to the recent work of Wang and Wang (2019) in the sense that: (ⅰ) for the critical case where $\Re_{0} = 1$, cholera-free steady state is globally asymptotically stable; (ⅱ) in a homogeneous case, the positive constant steady-state is globally asymptotically stable with additional condition when $\Re_{0}>1$. Our first result is achieved by proving the local asymptotic stability and global attractivity. Our second result is obtained by Lyapunov function.

    Citation: Xiaoqing Wu, Yinghui Shan, Jianguo Gao. A note on advection-diffusion cholera model with bacterial hyperinfectivity[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7398-7410. doi: 10.3934/mbe.2020378

    Related Papers:

  • This note gives a supplement to the recent work of Wang and Wang (2019) in the sense that: (ⅰ) for the critical case where $\Re_{0} = 1$, cholera-free steady state is globally asymptotically stable; (ⅱ) in a homogeneous case, the positive constant steady-state is globally asymptotically stable with additional condition when $\Re_{0}>1$. Our first result is achieved by proving the local asymptotic stability and global attractivity. Our second result is obtained by Lyapunov function.


    加载中


    [1] X. Wang, F. B. Wang, Impact of bacterial hyperinfectivity on cholera epidemics in a spatially heterogeneous environment, J. Math. Anal. Appl., 480 (2019), 123407. doi: 10.1016/j.jmaa.2019.123407
    [2] L. Cai, C. Modnak, J. Wang, An age-structured model for cholera control with vaccination, Appl. Math. Comput., 299 (2017), 127-140.
    [3] F. Brauer, Z. Shuai, P. van den Driessche, Dynamics of an age-of-infection cholera model, Math. Biosci. Eng., 10 (2013), 1335-1349. doi: 10.3934/mbe.2013.10.1335
    [4] K. Yamazaki, X. Wang, Global stability and uniform persistence of the reaction-convectiondiffusion cholera epidemic model, Math. Biosci. Eng., 14 (2017), 559-579.
    [5] J. Wang, J. Wang, Analysis of a reaction-diffusion cholera model with distinct dispersal rates in the human population, J. Dyn. Differ. Equations, 2020 (2020), 1-27.
    [6] J. Wang, F. Xie, T. Kuniya, Analysis of a reaction-diffusion cholera epidemic model in a spatially heterogeneous environment, Commun. Nonlinear Sci. Numer. Simul., 80 (2020), 104951. doi: 10.1016/j.cnsns.2019.104951
    [7] X. Zhang, H. Peng, Stationary distribution of a stochastic cholera epidemic model with vaccination under regime switching, Appl. Math. Lett., 102 (2020), 106095. doi: 10.1016/j.aml.2019.106095
    [8] W. Wang, X. Q. Zhao, Basic reproduction numbers for reaction-diffusion epidemic models, SIAM J. Appl. Dyn. Syst., 11 (2012), 1652-1673. doi: 10.1137/120872942
    [9] 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
    [10] R. Cui, K. Y. Lam, Y. Lou, Dynamics and asymptotic profiles of steady states of an epidemic model in advective environments, J. Differ. Equations, 263 (2017), 2343-2373. doi: 10.1016/j.jde.2017.03.045
    [11] 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
    [12] Y. Wu, X. Zou, Dynamics and profiles of a diffusive host-pathogen system with distinct dispersal rates, J. Differ. Equations, 264 (2018), 4989-5024. doi: 10.1016/j.jde.2017.12.027
    [13] Y. Yang, J. Zhou, C. Hsu, Threshold dynamics of a diffusive SIRI model with nonlinear incidence rate, J. Math. Anal. Appl., 478 (2019), 874-896. doi: 10.1016/j.jmaa.2019.05.059
    [14] X. Q. Zhao, Dynamical Systems in Population Biology, Springer, New York, 2003.
    [15] Z. Shuai, P. van den Driessche, Global dynamics of cholera models with differential infectivity, Math. Biosci., 234 (2011), 118-126. doi: 10.1016/j.mbs.2011.09.003
    [16] H. Zhang, J. Xia, P. Georgescu, Stability analyses of deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delay, Nonlinear Anal. Modell. Control, 22 (2017), 64-83.
    [17] Y. Yang, L. Zou, J. Zhou, C. H. Hsu, Dynamics of a waterborne pathogen model with spatial heterogeneity and general incidence rate, Nonlinear Anal. Real World Appl., 53 (2020), 103065. doi: 10.1016/j.nonrwa.2019.103065
    [18] H. L. Smith, H. R. Thieme, Dynamical Systems and Population Persistence, American Mathematical Society, Providence, 2011.
  • Reader Comments
  • © 2020 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(2273) PDF downloads(86) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog