On the Oscillatory Dynamical Behaviour of Epidemic Spreading in Fractal Media

M. A. BAB; E. V. ALBANO

JOURNAL OF PHYSICS. A - MATHEMATICAL AND GENERAL

Institut of Physics Publishing

Año: 2008 vol. 41 p. 450011 - 4500111

0305-4470

We present numerical evidence that dynamicl physical processes that develop a time-dependent characteristic length, and take place in fractal media exihibiting spatial discrete scale invariance (DSI) with funfamental scaling ratio b, may become coupled to the topology of the fractal leading to the observation of time DSI. The hallmark of time DSI is the observation of a log-periodic modulation of the dynamic or kinetic observables, which is characterized by a well-defined fundamental time scaling ratio. Both fundamental scaling ratios are linked according to b=tau^(1/z), where z is the dynamic exponent characteristic of the physical process. Specifically, we have studied the epidemic behaviour of the contact process (CP) in Sierpinski Carpets. The CP exhibits second-order irreversible phase transitions between an active regime and an absorbing state where the system is trapped without any escape possibility. We observed that relevant dynamic observables, such as the number of active sites, the survival probability of the epidemics and the mean square displacement of the epidemic from the origin, exhibit log-periodic modulations. By fitting the data we evaluate the fundamental time scaling ratio for various fractals and the corresponding dynamic exponents. Since, at criticality , from the mean square displacement an independent estimation of the dynamic exponent can be performed, in the excellent agreement with results obtained by using the conjetured relationship for the fundamental scaling ratios b and tau.