SIR model on a dynamical network and the endemic state of an infectious disease

M. DOTTORI; G. FABRICIUS

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2015 vol. 434 p. 25 - 35

0378-4371

In this work we performed a numerical study of an epidemic model thatmimics the endemic state of whooping cough in the pre-vaccine era. Weconsidered a stochastic SIR model on dynamical networks that involve localand global contacts among individuals and analysed the influence of thenetwork properties on the characterization of the quasi-stationary state. Wecomputed probability density functions (PDF) for infected fraction of individualsand found that they are well fitted by gamma functions, exceptedthe tails of the distributions that are q-exponentials. We also computed thefluctuation power spectra of infective time series for different networks. Wefound that network effects can be partially absorbed by rescaling the rateof infective contacts of the model. An explicit relation between the effectivetransmission rate of the disease and the correlation of susceptible individualswith their infective nearest neighbours was obtained. This relation quantifiesthe known screening of infective individuals observed in these networks. Wefinally discuss the goodness and limitations of the SIR model with homogeneousmixing and parameters taken from epidemiological data to describethe dynamic behaviour observed in the networks studied.