TY - JOUR

T1 - Stochastic fluctuations in the susceptible-infective-recovered model with distributed infectious periods

AU - Black, Andrew J.

AU - McKane, Alan J.

AU - Nunes, Ana

AU - Parisi, Andrea

PY - 2009/8/19

Y1 - 2009/8/19

N2 - We investigate a stochastic model of infection dynamics based on the Susceptible-Infective-Recovered (SIR) model, where the distribution of the recovery times can be tuned, interpolating between exponentially distributed recovery times, as in the standard SIR model, and recovery after a fixed infectious period. This is achieved by introducing L infective classes, as compared to 1 in the standard model. For large populations, the spectrum of fluctuations around the deterministic limit of the model can be computed analytically. The demographic stochasticity has the effect of transforming the decaying oscillations of the deterministic model into sustained oscillations in the stochastic formulation. We find that the amplification of these stochastic oscillations increases with L, as well as their coherence in frequency. For large values of L (of the order of 10 and greater), the height and position of the peak of the power spectra changes little and is described well by the model with fixed recovery period (L→). In this limit we give a closed-form expression for the power spectrum of fluctuations of infective individuals.

AB - We investigate a stochastic model of infection dynamics based on the Susceptible-Infective-Recovered (SIR) model, where the distribution of the recovery times can be tuned, interpolating between exponentially distributed recovery times, as in the standard SIR model, and recovery after a fixed infectious period. This is achieved by introducing L infective classes, as compared to 1 in the standard model. For large populations, the spectrum of fluctuations around the deterministic limit of the model can be computed analytically. The demographic stochasticity has the effect of transforming the decaying oscillations of the deterministic model into sustained oscillations in the stochastic formulation. We find that the amplification of these stochastic oscillations increases with L, as well as their coherence in frequency. For large values of L (of the order of 10 and greater), the height and position of the peak of the power spectra changes little and is described well by the model with fixed recovery period (L→). In this limit we give a closed-form expression for the power spectrum of fluctuations of infective individuals.

U2 - 10.1103/PhysRevE.80.021922

DO - 10.1103/PhysRevE.80.021922

M3 - Journal article

AN - SCOPUS:69449085803

VL - 80

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 2

M1 - 021922

ER -