PARENT SESSION
Contributed Oral Session 94: Toxicology and Disease : Viruses and Epidemics
Wednesday, August 10, 1:30 PM - 5:00 PM, Meeting Room 514 A, Level 5, Palais des congrès de Montréal
Seasonality, instability boundaries, and stochastic amplification in epidemics.
Alonso, David*,1, McKane, Alan2, Pascual, Mercedes1, 1 Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, Michigan, USA2 Theory Group, School of Physics and Astronomy, University of Manchester, Machester, UK
ABSTRACT- The relevance of demographically driven stochastic fluctuations in epidemics has been widely recognized since Barlett's early seminal work. In particular, it is known that demographic stochasticity can sustain cycles with the same characteristic frequency than that of the decaying oscillations towards the stable point attractor of the corresponding deterministic (ODE) system. In this paper, we qualify this observation and show that it does not generally hold. We present a theory to describe analytically the fluctuations produced by demographic stochasticity in epidemic models. We apply this theory to the Susceptible-Infected-Recovered model for infectious diseases with immigration. In particular, we derive the corresponding predicted power spectra of both infective and susceptible individuals and conditions under which large and sustained cyclic stochastic fluctuations are expected. We apply this approach to measles data in England and Wales. We observe that typical parameter values for several infectious diseases lie within a region of the parameter space characterized by strong stochastic amplification close to an instability boundary. Our results suggest an alternative simple explanation for the major dynamical transitions in epidemics, from regular to irregular cycles. This explanation is based exclusively on the stochastic description of the system, is robust to seasonal forcing, and requires low immigration.
Key words: epidemics, SIR-model, stochastic-amplification, seasonality