  Epidemiological processes are studied within a recently proposed hierarchical
network model using the susceptible-infected-refractory dynamics of an
epidemic. Within the network model, a population may be characterized by $H$
independent hierarchies or dimensions, each of which consists of groupings of
individuals into layers of subgroups. Detailed numerical simulations reveal
that for $H>1$, global spreading results regardless of the degree of homophily
of the individuals forming a social circle. For H=1, a transition from global
to local spread occurs as the population becomes decomposed into increasingly
homophilous groups. Multiple dimensions in classifying individuals (nodes) thus
make a society (computer network) highly susceptible to large scale outbreaks
of infectious diseases (viruses).
