Stochastic amplification in an epidemic model with seasonal forcing.
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 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 whooping cough and measles epidemics.
Black
Andrew J
AJ
Theoretical Physics Group, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK. andrew.black@postgrad.manchester.ac.uk
McKane
Alan J
AJ
D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D058872:Epidemics / Q000706:statistics & numerical data; D006801:Humans; D008390:Markov Chains; D008457:Measles / Q000453:epidemiology; D008954:Models, Biological; D012621:Seasons; D014917:Whooping Cough / Q000453:epidemiology