Biology – Quantitative Biology – Populations and Evolution
Scientific paper
2011-12-20
Theoretical Population Biology, 81, 223-231 (2012)
Biology
Quantitative Biology
Populations and Evolution
29 pages, 5 figures
Scientific paper
10.1016/j.tpb.2012.01.002
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 system 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.
Qian Hong
Qian Min
Wang Jia-Zeng
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