Article explained:

Impact of human mobility on the periodicities and mechanisms underlying measles dynamics
Ramona Marguta and Andrea Parisi
J. R. Soc. Interface, 12, 20141317 (2015) doi: 10.1098/rsif.2014.1317 [Article explained]

Can we understand and visualize the spread of infectious diseases in large areas using detailed resolution? This has been the main objective that led us to produce geographically detailed simulations of measles spread in the British Isles in conditions corresponding to those of pre-vaccination era (1944-66).

Measles is a well studied disease: several publications have been devoted to its dynamics and the mechanisms that control the periodical outbreaks of the disease, but the human mobility factor has not been thoroughly explored so far. However, some key mechanisms depend on mobility: in fact mobility is a key ingredient in explaining the recurrent outbreaks occurring in low populated areas.

By considering a detailed geographical description of human settlements as well as human mobility, we have been able to uncover the link between human mobility, the frequency of measles outbreaks and the mechanisms underlying its dynamics. Specifically we have seen that different mechanisms are at work depending of the intensity of human mobility and the size of the local population. We have also seen that, when we consider the whole of the British Isles, the resulting sequence of outbreaks might have characteristics that differ from what is observed locally: in other words, what is observed at the global level has a complex relation with what occurs in the multeplicity of cities and low populated areas that constitute the British Isles.

So, how do we build our simulations? First we start from the Gridded Population of the World database: this provides a description of the world as a grid of cells with 2.5 arc-minutes (roughly 3.5 km for the British Isles). We focus in particular on the British Isles as they are... isles, and hence separated from continental Europe. This means that mobility with the continent can be (to some extent) ignored. In fact, simulations show that even ignoring the rest of the world, the disease is self-sustained in the British Isles even for low levels of human mobility!

On top of this gridded geographical description there is human mobility. We use one of the latest models, the so called radiation model, to simulate it. Individuals are moved to different cells where the stay for one day and then move back. Although we do not aim to simulate the true movement of individuals, yet we carefully build the details so that the statistical features of moving individuals reflect realism.

The simulation program is parallelized, that means that the workload is distributed on multiple machines working in parallel (a cluster): such a computer can be extended by adding new machines as required. This translates into having a simulation program that can be used to investigate epidemiological models of unlimited complexity! This is a feature that we plan to exploit in the future.

Finally, the algorithm used to parallelize our simulation is, on its own, innovative as we use a well known algorithm (simulated annealing) and make it work fast for our purposes using a multi-level coarsening technique that speeds up the partitioning procedure to optimize the distribution of the workload to the machines in the cluster.

How do our simulations look like? Here is an example: