Synchronization of infections spread processes in populations interacting: Modeling by lattices of cellular automata

Abstract

Purpose. Study of synchronization of oscillations in ensembles of probabilistic cellular automata that simulate the spread of infections in biological populations. Method. Numerical simulation of the square lattice of cellular automata by means of the Monte Carlo method, investigation of synchronization of oscillations by time-series analisys and by the coherence function. Results. The effect has been found of synchronization of irregular oscillations, similar to the phenomenon of synchronization of chaos in dynamical systems. It is shown that the coupled lattices of cellular automata can demonstrate the effect of phase locking, as well as the tuning of the main frequencies in the oscillation spectra; at strong coupling they also can demonstrate an almost complete synchronization regime. Discussion. The most interesting result of the work is the revealed similarity of the phenomenon of chaos synchronization, which is well known for deterministic systems, with synchronization of irregular oscillations in interacting stochastic ensembles, whose behavior is determined exclusively by probabilistic laws. At the same time, the interaction algorithm, which has been used in the modeling is too idealized, becouse it does not consider the finite speed of diffusion processes. Taking the last into account will probably lead to more complex types of synchronization that has been found in the research.

Keywords

• synchronization
• cellular automata lattices
• sirs model
• population dynamics