Optimizing Hybrid Spreading in Metapopulations

Epidemic spreading phenomena are ubiquitous in nature and society. Examples include the spreading of diseases, information, and computer viruses. Epidemics can spread by \textit{local spreading}, where infected nodes can only infect a limited set of direct target nodes and \textit{global spreading}, where an infected node can infect every other node. In reality, many epidemics spread using a hybrid mixture of both types of spreading. In this study we develop a theoretical framework for studying hybrid epidemics, and examine the optimum balance between spreading mechanisms in terms of achieving the maximum outbreak size. In a metapopulation, made up of many weakly connected subpopulations, we show that one can calculate an optimal tradeoff between local and global spreading which will maximise the extent of the epidemic. As an example we analyse the 2008 outbreak of the Internet worm Conficker, which uses hybrid spreading to propagate through the internet. Our results suggests that the worm would have been even more infectious if it had optimised the balance between modes of spreading. Our results suggest new strategies for maximising beneficial epidemics (e.g. disseminating information) and estimating the worst outcome of hybrid epidemics which damage health or economic activity.