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

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.

• Publication year

  2011

• Venue

  Theoretical Population Biology

• Publication date

  2011-12-20

• Fields of study

  Biology, Mathematics, Medicine

• Identifiers
  DOI 10.1016/j.tpb.2012.01.002arXiv 1112.4768PMID 22273833
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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