Modeling human interactions and the dynamics of epidemic spreading

Respiratory infections, such as the flu, spread mainly through face-to-face contacts between individuals.  Recent development of portable and cheap radio-frequency receptor/emitters has enabled time-resolved measurement of physical interactions. Measured data, typically represented by a temporal network, reveal the heterogeneous dynamics at play and can be used to improve models of social behavior and inform realistic simulations of epidemic spreading.

I will present some of our recent advances along these directions. First, I present a generalized version of the Doob-Gillespie algorithm that can be used for simulation of stochastic contagion processes on temporal networks. This temporal Gillespie algorithm is stochastically exact, and up to several orders of magnitude faster than traditional methods based on rejection sampling.

Second, I present a simple generative modeling framework for social interactions in a well-mixed population. It allows us to study how heterogeneous dynamics emerge as the result of different memory mechanisms at the level of individuals. We propose four individual mechanisms, which together result in generally heterogeneous network dynamics, notably of contact and inter-contact durations and frequencies of contacts per link, as observed in empirical contact networks. Our modeling framework thus enables us to study the individual effect of heterogeneities on the propagation of contagion processes.

I finally discuss our current efforts to include social groupings and different physical locations, which constrain who can interact with whom, in the above model. This augmented model can be applied to investigate the validity of the assumptions of homogeneity underlying the popular metapopulation models of epidemic spreading, and to study dynamic sampling effects.