Fractional diffusion emulates a human mobility network during a simulated disease outbreak

January 28, 2016

Abstract: 

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between contact nodes. In some cases, transport can be parameterized with gravity-type models or approximated by a diffusive random walk. As a alternative, we have isolated intranational commercial air traffic as a case study for the utility of non-diffusive, heavy-tailed transport models. We implemented new stochastic simulations of a prototypical influenza-like infection, focusing on the dense, highly-connected United States air travel network. We show that mobility on this network can be described mainly by a power law, in agreement with previous studies. Remarkably, we find that the global evolution of an outbreak on this network is accurately reproduced by a two-parameter space-fractional diffusion equation, such that those parameters are determined by the air travel network.

Figure 2. (a) and (b) Outbreak of a stochastic seasonal SIS influenza-like infection on the USA flight network, with origins either in Atlanta (ATL) (a) or Colorado Springs (COS) (b). The seasonal force of infection is scaled using the Google Flu Trends timeseries for infectivity β(t), where the baseline β0 = 12 and γ = 3. After some time (top to bottom), the disease propagates throughout the network and tends to fadeout due to stochastic fluctuations and dilution. The colorbar shows the number of infected population units for each node, Ι(t). (c-d) Time course of SIS outbreaks for the networks in the above panels, showing the average infected for the seven most connected hubs, the average infected for all other nodes, and the specific nodes ATL and COS.