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DY: Fachverband Dynamik und Statistische Physik

DY 21: Statistical Physics in Biological Systems (joint session DY/ BP/CPP)

DY 21.1: Vortrag

Dienstag, 21. März 2017, 14:00–14:15, ZEU 118

Epidemic spread in heterogeneous populations - Propagation of uncertainty and linear-noise approximation — •Francisco Herrerías-Azcué and Tobias Galla — School of Physics and Astronomy, The University of Manchester, Manchester, UK

The assumption of homogeneity in classic epidemic models is known to be far from realistic; Different susceptibilities may arise from gene expression and strain mutation. We explore the effects of heterogeneity in susceptibility and infectivity on the stochastic susceptible-infective-recovered (SIR) model of epidemic spread. Our focus is on understanding how these heterogeneities and uncertainties propagate to long-term periodic outbreaks. To do so, we study a structured population consisting of sub-classes with different susceptibilities and infectivities. These are assigned at birth, drawn from underlying fixed distributions.

We show how the system can be reduced to a four dimensional set of equations at the fixed point in the deterministic limit, independent of the number of sub-classes, and we derive the Langevin dynamics characterising fluctuations about this fixed point. To characterise the resulting noise-induced cycles we calculate the power spectra of fluctuations, and determine the features of the distributions of susceptibilities and infectivities shaping the quasi-cycles. In particular we explore how the mean or spread of susceptibilities affect the magnitude of the epidemic, and the period of outbreak cycles. We also investigate the dynamic behaviour and relative phase lag of different sub-populations during the outbreaks.