New paper with @stevenstrogatz is online!
We ask: If an infectious disease mutates as it propagates, what fraction of the population will catch the mutant strain? How does this depend on the structure of the network which the contagion is spreading on? 1/ https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.033005

To estimate this impact of mutant contagion, we had to understand what the paths of who-infects-whom in the network look like. We can visualize the path taken by the contagion as an Epidemic Tree -- a family tree of infections. 2/

In this family tree [b) in image], patient 0 is in the top row, the people patient 0 infected are in the second row, etc. If a mutation occurs at some node (node B in the figure), who will be affected by this? Every descendant of B. 3/

So the impact of a mutation event depends on the structure of the Epidemic Tree. The Epidemic Tree, in turn, is shaped by the underlying contact network. So the expected impact of mutant contagion should be sensitive to the underlying network structure, right? 4/

Actually, we show that the expected impact of a mutant contagion is similar for a wide range of contact networks. The function describing the probability that a mutation will affect d people has the same shape for all of these networks. 5/

Why? Our calculations suggest this is because all these networks are ‘infinite dimensional’. Conveniently, many real-world networks are infinite dimensional, too. For example, human contact networks and online social networks. 6/

Indeed, we find that simulations of a contagion spreading on a small Facebook network gives rise to the same impact of mutant contagion. 7/

… and simulations on a two-dimensional grid gives rise to a completely different impact of mutant contagion. 8/

One interesting feature of this probability distribution of the impact of mutant contagion spreading on infinite-dimension networks is that it is heavy-tailed. Occasionally, mutations get ‘lucky’ and reach large fractions of the network. 9/

There’s much more to be learned. Our model is as simple as it can be and therefore leaves out many things that are important in realistic scenarios: heterogeneities in susceptibility, infectiousness, immunity, and so on. 10/

It’s been amazing to work on this project with @stevenstrogatz . I am grateful to all the nice people at the Center for Applied Mathematics, Cornell University - I look very much forward to joining as a postdoc. 11/11