Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 5: Statistical Physics of Biological Systems II (organised by DY)

DY 5.2: Talk

Monday, March 14, 2011, 14:30–14:45, HÜL 186

Stochastic amplification in an epidemic model with seasonal forcing — •Andrew Black and Alan McKane — Theoretical Physics Group, University of Manchester, UK

Stochastic models, subject to external forcing, can capture the regular oscillatory patterns of childhood epidemics, such as measles and whooping cough, but so far the mechanisms generating these pattens have not been well understood. We study the stochastic susceptible-infected-recovered (SIR) model with time-dependent forcing using analytic techniques which allow us to disentangle the interaction of stochasticity and external forcing. The model is formulated as a continuous time Markov process, which is decomposed into a deterministic dynamics together with stochastic corrections, by using an expansion in inverse system size. The forcing induces a limit cycle in the deterministic dynamics, and with the use of Floquet theory, a complete analysis of the fluctuations about this time-dependent solution is given. This analysis is applied when the limit cycle is annual, and after a period-doubling when it is biennial. The comprehensive nature of our approach allows us to give a coherent picture of the dynamics which unifies past work, but which also provides a systematic method for predicting the periods of oscillations seen in both whooping cough and measles epidemics.