Proximity Networks and Epidemics

Disease spread in most biological populations requires the proximity of agents. In populations where the individuals have spatial mobility, the contact graph is generated by the "collision dynamics" of the agents, and thus the evolution of epidemics couples directly to the spatial dynamics of the population. We first briefly review the properties and the methodology of an agent-based simulation (EPISIMS) to model disease spread in realistic urban dynamic contact networks. Using the data generated by this simulation, we introduce the notion of dynamic proximity networks which takes into account the relevant time scales for disease spread: contact duration, infectivity period and rate of contact creation. This approach promises to be a good candidate for a unified treatment of epidemic types that are driven by agent collision dynamics. In particular, using a simple model, we show that it can can account for the observed qualitative differences between the degree distributions of contact graphs of diseases with short infectivity period (such as air-transmitted diseases) or long infectivity periods (such as HIV).