TY - JOUR
T1 - Fluctuations and oscillations in a simple epidemic model
AU - Rozhnova, G.
AU - Nunes, A.
PY - 2009/4/1
Y1 - 2009/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=66049138052&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.79.041922
DO - 10.1103/PhysRevE.79.041922
M3 - Article
AN - SCOPUS:66049138052
SN - 1539-3755
VL - 79
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 4
M1 - 041922
ER -