IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v81y2012i3p223-231.html
   My bibliography  Save this article

Circular stochastic fluctuations in SIS epidemics with heterogeneous contacts among sub-populations

Author

Listed:
  • Wang, Jia-Zeng
  • Qian, Min
  • Qian, Hong

Abstract

The conceptual difference between equilibrium and non-equilibrium steady state (NESS) is well established in physics and chemistry. This distinction, however, is not widely appreciated in dynamical descriptions of biological populations in terms of differential equations in which fixed point, steady state, and equilibrium are all synonymous. We study NESS in a stochastic SIS (susceptible–infectious–susceptible) system with heterogeneous individuals in their contact behavior represented in terms of subgroups. In the infinite population limit, the stochastic dynamics yields a system of deterministic evolution equations for population densities; and for very large but finite systems a diffusion process is obtained. We report the emergence of a circular dynamics in the diffusion process, with an intrinsic frequency, near the endemic steady state. The endemic steady state is represented by a stable node in the deterministic dynamics. As a NESS phenomenon, the circular motion is caused by the intrinsic heterogeneity within the subgroups, leading to a broken symmetry and time irreversibility.

Suggested Citation

  • Wang, Jia-Zeng & Qian, Min & Qian, Hong, 2012. "Circular stochastic fluctuations in SIS epidemics with heterogeneous contacts among sub-populations," Theoretical Population Biology, Elsevier, vol. 81(3), pages 223-231.
    • Handle: RePEc:eee:thpobi:v:81:y:2012:i:3:p:223-231
    DOI: 10.1016/j.tpb.2012.01.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580912000044
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2012.01.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 2000. "Scale-free characteristics of random networks: the topology of the world-wide web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 69-77.
    2. Wang, Jia-zeng & Liu, Zeng-rong & Xu, Jianhua, 2007. "Epidemic spreading on uncorrelated heterogenous networks with non-uniform transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 715-721.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Jia-Zeng & Peng, Wei-Hua, 2020. "Fluctuations for the outbreak prevalence of the SIR epidemics in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    2. Garrett Jenkinson & John Goutsias, 2014. "Intrinsic Noise Induces Critical Behavior in Leaky Markovian Networks Leading to Avalanching," PLOS Computational Biology, Public Library of Science, vol. 10(1), pages 1-15, January.
    3. Xue, Xiaofeng, 2013. "Contact processes with random connection weights on regular graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4749-4759.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ruiz Vargas, E. & Mitchell, D.G.V. & Greening, S.G. & Wahl, L.M., 2014. "Topology of whole-brain functional MRI networks: Improving the truncated scale-free model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 151-158.
    2. Giacomello, Giampiero & Picci, Lucio, 2003. "My scale or your meter? Evaluating methods of measuring the Internet," Information Economics and Policy, Elsevier, vol. 15(3), pages 363-383, September.
    3. Ormerod, Paul & Roach, Andrew P, 2004. "The Medieval inquisition: scale-free networks and the suppression of heresy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(3), pages 645-652.
    4. Castagna, Alina & Chentouf, Leila & Ernst, Ekkehard, 2017. "Economic vulnerabilities in Italy: A network analysis using similarities in sectoral employment," GLO Discussion Paper Series 50, Global Labor Organization (GLO).
    5. Pascal Billand & Christophe Bravard & Sudipta Sarangi, 2011. "Resources Flows Asymmetries in Strict Nash Networks with Partner Heterogeneity," Working Papers 1108, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    6. Zhu, Yu-Xiao & Cao, Yan-Yan & Chen, Ting & Qiu, Xiao-Yan & Wang, Wei & Hou, Rui, 2018. "Crossover phenomena in growth pattern of social contagions with restricted contact," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 408-414.
    7. Linyuan Lü & Yi-Cheng Zhang & Chi Ho Yeung & Tao Zhou, 2011. "Leaders in Social Networks, the Delicious Case," PLOS ONE, Public Library of Science, vol. 6(6), pages 1-9, June.
    8. Zio, Enrico, 2016. "Challenges in the vulnerability and risk analysis of critical infrastructures," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 137-150.
    9. Tamás Sebestyén & Dóra Longauer, 2018. "Network structure, equilibrium and dynamics in a monopolistically competitive economy," Netnomics, Springer, vol. 19(3), pages 131-157, December.
    10. Wang, Huan & Xu, Chuan-Yun & Hu, Jing-Bo & Cao, Ke-Fei, 2014. "A complex network analysis of hypertension-related genes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 166-176.
    11. Wang, Yi & Cao, Jinde & Jin, Zhen & Zhang, Haifeng & Sun, Gui-Quan, 2013. "Impact of media coverage on epidemic spreading in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5824-5835.
    12. Elisa Letizia & Fabrizio Lillo, 2017. "Corporate payments networks and credit risk rating," Papers 1711.07677, arXiv.org, revised Sep 2018.
    13. Dunia López-Pintado, 2006. "Contagion and coordination in random networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 371-381, October.
    14. Li, Jianyu & Zhou, Jie, 2007. "Chinese character structure analysis based on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 629-638.
    15. Wang, Haiying & Wang, Jun & Small, Michael & Moore, Jack Murdoch, 2019. "Review mechanism promotes knowledge transmission in complex networks," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 113-125.
    16. Laureti, Paolo & Moret, Lionel & Zhang, Yi-Cheng, 2005. "Aggregating partial, local evaluations to achieve global ranking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(3), pages 705-712.
    17. Jean-Marc Luck & Anita Mehta, 2023. "Evolution of grammatical forms: some quantitative approaches," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-15, February.
    18. Seyed Soheil Hosseini & Nick Wormald & Tianhai Tian, 2019. "A Weight-based Information Filtration Algorithm for Stock-Correlation Networks," Papers 1904.06007, arXiv.org.
    19. Wang, Yanhui & Bi, Lifeng & Lin, Shuai & Li, Man & Shi, Hao, 2017. "A complex network-based importance measure for mechatronics systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 180-198.
    20. Chan, N.H. & Cheung, Simon K.C. & Wong, Samuel P.S., 2020. "Inference for the degree distributions of preferential attachment networks with zero-degree nodes," Journal of Econometrics, Elsevier, vol. 216(1), pages 220-234.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:thpobi:v:81:y:2012:i:3:p:223-231. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/intelligence .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.