Fluctuations and oscillations in a simple epidemic model.

Departamento de Física and Centro de Física Teórica e Computacional, Faculdade de Ciências da Universidade de Lisboa, P-1649-003 Lisboa Codex, Portugal.
Physical Review E (Impact Factor: 2.31). 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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