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

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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