Search Advanced

Mathematical Biosciences and Engineering

2014, Volume 11, Issue 3: 641-665. doi: 10.3934/mbe.2014.11.641
Previous Article Next Article

Global stability of an age-structured cholera model

  • 1.
    Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094
  • 2.
    Department of Mathematics, Xinyang Normal University, Xinyang 464000
  • Received: 01 November 2012 Accepted: 29 June 2018 Published: 01 January 2013

  • MSC : Primary: 92B05, 92D30.

  • In this paper, an age-structured epidemicmodel is formulated to describe the transmission dynamics ofcholera. The PDE model incorporates direct and indirect transmissionpathways, infection-age-dependent infectivity and variable periodsof infectiousness. Under some suitable assumptions, the PDE modelcan be reduced to the multi-stage models investigated in theliterature. By using the method of Lyapunov function, we establishedthe dynamical properties of the PDE model, and the results show thatthe global dynamics of the model is completely determined by thebasic reproduction number $\mathcal R_0$: if $\mathcal R_0 < 1$the cholera dies out, and if $\mathcal R_0>1$ the disease will persist at the endemicequilibrium. Then the global results obtained for multi-stage modelsare extended to the general continuous age model.

    Citation: Jianxin Yang, Zhipeng Qiu, Xue-Zhi Li. Global stability of an age-structured cholera model[J]. Mathematical Biosciences and Engineering, 2014, 11(3): 641-665. doi: 10.3934/mbe.2014.11.641

    Related Papers:

  • In this paper, an age-structured epidemicmodel is formulated to describe the transmission dynamics ofcholera. The PDE model incorporates direct and indirect transmissionpathways, infection-age-dependent infectivity and variable periodsof infectiousness. Under some suitable assumptions, the PDE modelcan be reduced to the multi-stage models investigated in theliterature. By using the method of Lyapunov function, we establishedthe dynamical properties of the PDE model, and the results show thatthe global dynamics of the model is completely determined by thebasic reproduction number $\mathcal R_0$: if $\mathcal R_0 < 1$the cholera dies out, and if $\mathcal R_0>1$ the disease will persist at the endemicequilibrium. Then the global results obtained for multi-stage modelsare extended to the general continuous age model.


    加载中
    [1] Lancet, 377 (2011), 1248-1255.
    [2] J. Math. Biol., 28 (1998), 365-382.
    [3] Wiley, New York, 2000.
    [4] J. Diff. Equs., 218 (2005), 292-324.
    [5] Math. Biosci., 76 (1985), 69-86.
    [6] Amer. Natur., 111 (1977), 135-143.
    [7] Mathematical Surveys and Monographs 25, American Mathematical Society, Providence, RI, 1988.
    [8] SIAM J. Math. Anal., 20 (1989), 388-395.
    [9] Cambridge University Press, Cambridge, 1988.
    [10] SIAM J. Appl. Math., 72 (2012), 25-38.
    [11] Applied Mathematics Monographs 7, comitato nazionale per le scienze matematiche, Consiglio Nazionale delle Ricerche (C. N. R), Giardini, Pisa, 1995.
    [12] Math. Popul. Studi., 17 (1988), 47-77.
    [13] Proc. Roy. Soc. Lond. B, 268 (2001), 985-993.
    [14] Theor. Popul. Biol., 60 (2001), 59-71.
    [15] Electron. J. Diff. Equs., 65 (2001), 1-35.
    [16] Communications on Pure and Applied Analysis, 3 (2004), 695-727.
    [17] SIAM J. Math. Anal., 37 (2005), 251-275.
    [18] Diff. Integr. Equs., 19 (2006), 573-600.
    [19] Appl. Anal., 89 (2010), 1109-1140.
    [20] SIAM J. Appl. Math., 73 (2013), 1058-1095.
    [21] J. Math. Biol., 39 (1999), 471-492.
    [22] Math. Biosci., 234 (2011), 118-126.
    [23] Bull. Math. Biol., 74 (2010), 2423-2445.
    [24] Diff. Integr. Equs., 3 (1990), 1035-1066.
    [25] SIAM J. Appl. Math., 53 (1993), 1447-1479.
    [26] 2010. Available from: http://www.math.wm.edu/~jptian/preprints/pr-7-ode-cholera.pdf.
    [27] Math. Biosci., 232 (2011), 31-41.
    [28] Bull. Math. Biol., 72 (2010), 1506-1533.
    [29] Math. Biosci., 180 (2002), 29-48.
    [30] Marcel Dekker, New York, 1985.
  • Reader Comments
  • © 2014 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
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(2882) PDF downloads(663) Cited by(32)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog