Effects of variable neighbourhood on spreading processes

A theoretical framework for the description of Susceptible-Infected-Removed (SIR) spreading processes with synergistic transmission of infection on a lattice is developed. The model incorporates explicitly the effects of a time-dependent environment on the transmission of infection between hosts. Exact solution of the model shows that time-dependence of the neighbourhood of recipient hosts is a key factor for synergistic spreading processes. It is demonstrated that the higher the connectivity of a lattice, the more prominent is the effect of synergy on spread.