  Epidemic spreading phenomena are ubiquitous in nature and society. Examples
include the spreading of diseases, information, and computer viruses. Epidemics
can spread by local spreading, where infected nodes can only infect a limited
set of direct target nodes and 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.
We show the existence of critically hybrid epidemics where neither spreading
mechanism alone can cause a noticeable spread but a combination of the two
spreading mechanisms would produce an enormous outbreak. Our results provide
new strategies for maximising beneficial epidemics and estimating the worst
outcome of damaging hybrid epidemics.
