Spatio-temporal dynamics of random transmission events: from information sharing to epidemic spread

Abstract

Random transmission events between individuals occurring at short scales control patterns emerging at much larger scales in natural and artificial systems. Examples range from the spatial propagation of an infectious pathogen in an animal population to the spread of misinformation in online social networks or the sharing of target locations between robot units in a swarm. Despite the ubiquity of information transfer events, a general methodology to quantify spatio-temporal transmission processes has remained elusive. The challenge in predicting when and where information is passed from one individual to another stems from the limited number of analytic approaches and from the large fluctuations and inherent computational cost of stochastic simulation outputs, the main theoretical tool available to study such processes so far. Here we overcome these limitations by developing an analytic theory of transmission dynamics between randomly moving agents in arbitrary spatial domains and with arbitrary information transfer efficiency. We move beyond well-known approximations employed to study reaction diffusion phenomena, such as the motion and reaction limited regimes, by quantifying exactly the mean reaction time in presence of multiple heterogeneous reactive locations. To demonstrate the wide applicability of our theory we employ it in different scenarios. We show how the type of spatial confinement may change by many orders of magnitude the time scale at which transmission occurs. When acquiring information represents the ability to capture, we use our formalism to uncover counterintuitive evasive strategies in a predator–prey contest between territorial animals. When information transmission represents the transfer of an infectious pathogen, we consider a population with susceptible, infected and recovered individuals that move and pass infection upon meeting and predict analytically the basic reproduction number. Finally we show how to apply the transmission theory semi-analytically when the topology of where individuals move is that of a network.