Effects of variable neighbourhood on spreading processes

TL;DR

This paper develops a theoretical framework for SIR spreading processes considering variable neighborhoods and environmental effects, revealing how connectivity influences synergy in infection spread.

Contribution

It introduces a model that explicitly accounts for time-dependent neighborhoods and environmental factors in synergistic infection spreading on lattices.

Findings

Time-dependent neighborhoods are crucial for synergistic spreading.

Higher lattice connectivity amplifies the effect of synergy.

Exact solutions highlight the importance of environment in transmission dynamics.

Abstract

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.