Circular Stochastic Fluctuations in SIS Epidemics with Heterogeneous Contacts Among Sub-populations

TL;DR

This paper investigates the non-equilibrium steady states in a stochastic SIS epidemic model with heterogeneous contacts, revealing a circular dynamic behavior caused by subgroup heterogeneity and intrinsic system frequency.

Contribution

It introduces a novel analysis of NESS in heterogeneous SIS models, highlighting circular dynamics and time irreversibility arising from subgroup heterogeneity.

Findings

Circular dynamics with intrinsic frequency near endemic steady state

Heterogeneity causes broken symmetry and time irreversibility

Diffusion process captures finite population stochastic effects

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 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.