Search Advanced

Mathematical Biosciences and Engineering

2015, Volume 12, Issue 3: 565-584. doi: 10.3934/mbe.2015.12.565
Previous Article Next Article

Network-level reproduction number and extinction threshold for vector-borne diseases

  • 1.
    Kansas State Epicenter, Department of Electrical & Computer Engineering, Kansas State University, Manhattan, KS 66506
  • Received: 01 June 2014 Accepted: 29 June 2018 Published: 01 January 2015

  • MSC : Primary: 92B30; Secondary: 62P10, 92B05.

  • The basic reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or not. Thresholds for disease extinction contribute crucial knowledge of disease control, elimination, and mitigation of infectious diseases. Relationships between basic reproduction numbers of two deterministic network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding stochastic continuous-time Markov chain models are derived under some assumptions. Numerical simulation results for malaria and Rift Valley fever transmission on heterogeneous networks are in agreement with analytical results without any assumptions, reinforcing that the relationships may always exist and proposing a mathematical problem for proving existence of the relationships in general. Moreover, numerical simulations show that the basic reproduction number does not monotonically increase or decrease with the extinction threshold. Consistent trends of extinction probability observed through numerical simulations provide novel insights into mitigation strategies to increase the disease extinction probability. Research findings may improve understandings of thresholds for disease persistence in order to control vector-borne diseases.

    Citation: Ling Xue, Caterina Scoglio. Network-level reproduction number and extinction threshold for vector-borne diseases[J]. Mathematical Biosciences and Engineering, 2015, 12(3): 565-584. doi: 10.3934/mbe.2015.12.565

    Related Papers:

  • The basic reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or not. Thresholds for disease extinction contribute crucial knowledge of disease control, elimination, and mitigation of infectious diseases. Relationships between basic reproduction numbers of two deterministic network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding stochastic continuous-time Markov chain models are derived under some assumptions. Numerical simulation results for malaria and Rift Valley fever transmission on heterogeneous networks are in agreement with analytical results without any assumptions, reinforcing that the relationships may always exist and proposing a mathematical problem for proving existence of the relationships in general. Moreover, numerical simulations show that the basic reproduction number does not monotonically increase or decrease with the extinction threshold. Consistent trends of extinction probability observed through numerical simulations provide novel insights into mitigation strategies to increase the disease extinction probability. Research findings may improve understandings of thresholds for disease persistence in order to control vector-borne diseases.


    加载中
    [1] Journal of Biological Dynamics, 6 (2012), 590-611.
    [2] Mathematical Biolosciences, 243 (2013), 99-108.
    [3] Lecture Notes in Control and Information Sciences, 294 (2003), 135-142.
    [4] American Journal of Public Health, 39 (1949), p1592.
    [5] PloS ONE, 5 (2010), e13796.
    [6] Mathematical Biosciences, 222 (2009), 109-116.
    [7] Bulletin of Entomological Research, 89 (1999), 35-39.
    [8] Bulletin of Mathematical Biology, 70 (2008), 1272-1296.
    [9] Wiley, Chichester, 2000.
    [10] Journal of Mathematical Biology, 28 (1990), 365-382.
    [11] Contributions to Epidemiology and Biostatistics, 3 (1981), 77-82.
    [12] Annual Review of Entomology, 44 (1999), 51-75.
    [13] American Journal of Tropical Medicine and Hygiene, 22 (1973), 270-277.
    [14] Journal of Theoretical Biology, 255 (2008), 16-25.
    [15] Journal of the American Mosquito Control Association, 1 (1985), 530-532.
    [16] in Network Science (eds. E. Estrada, M. Fox, D. Higham and G. Oppo), Springer, (2010), 51-84.
    [17] Princeton University Press, 2008.
    [18] Bulletin of Mathematical Biology, 75 (2013), 1157-1180.
    [19] Journal of the Royal Society Interface, 4 (2007), 851-863.
    [20] American Journal of Tropical Medicine and Hygiene, 26 (1977), 547-552.
    [21] Centers for Disease Control and Prevention, 1993.
    [22] Preventive Veterinary Medicine, 92 (2009), 341-350.
    [23] PhD thesis, Institut für Mathematik der Unversität Potsdam, Germany, 2010.
    [24] in Handbook of Zoonoses (ed. G. Beran), $2^{nd}$ edition, Section B: Viral, CRC Press, Inc., Boca Raton, Fl, (1994), 125-138.
    [25] U.S. Department of Health and Human Services, Atlanta, GA, 1993.
    [26] Saunders, 2001.
    [27] Proceedings of the Royal Society B: Biological Sciences, 270 (2003), 1359-1364.
    [28] Nature, 87 (1911), 466-467.
    [29] Journal of mathematical biology, 67 (2013), 1067-1082.
    [30] Journal of Medical Entomology, 24 (1987), 11-18.
    [31] Journal of the American Mosquito Control Association, 4 (1988), 94-96.
    [32] Journal of Medical Entomology, 25 (1988), 262-266.
    [33] Mathematical biosciences, 180 (2002), 29-48.
    [34] Proceedings of the Royal Society B: Biological Sciences, 276 (2009), 469-476.
    [35] Mathematical Biosciences, 243 (2013), 67-80.
  • Reader Comments
  • © 2015 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(3026) PDF downloads(525) Cited by(2)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog