Fluctuations and oscillations in a simple epidemic model

University of Lisbon, Lisboa, Lisbon, Portugal
Physical Review E (Impact Factor: 2.33). 05/2009; 79(4 Pt 1):041922. DOI: 10.1103/PhysRevE.79.041922
Source: PubMed

ABSTRACT We show that the simplest stochastic epidemiological models with spatial correlations exhibit two types of oscillatory behavior in the endemic phase. In a large parameter range, the oscillations are due to resonant amplification of stochastic fluctuations, a general mechanism first reported for predator-prey dynamics. In a narrow range of parameters that includes many infectious diseases which confer long lasting immunity the oscillations persist for infinite populations. This effect is apparent in simulations of the stochastic process in systems of variable size and can be understood from the phase diagram of the deterministic pair approximation equations. The two mechanisms combined play a central role in explaining the ubiquity of oscillatory behavior in real data and in simulation results of epidemic and other related models.

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    • "In discrete-time models, global oscillations have been reported [19– 22] and understood analytically [23]. In continuous-time models, the situation is different: in the standard SIRS model with diffusive coupling [24], global oscillations seem not to be stable, even in the favorable condition of global or random coupling [24] [25] [26] [27]. "
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