  Traditional mathematical models of epidemic disease had for decades
conventionally considered static structure for contacts. Recently, an upsurge
of theoretical inquiry has strived towards rendering the models more realistic
by incorporating the temporal aspects of networks of contacts, societal and
online, that are of interest in the study of epidemics (and other similar
diffusion processes). However, temporal dynamics have predominantly focused on
link fluctuations and nodal activities, and less attention has been paid to the
growth of the underlying network. Many real networks grow: online networks are
evidently in constant growth, and societal networks can grow due to migration
flux and reproduction. The effect of network growth on the epidemic properties
of networks is hitherto unknown---mainly due to the predominant focus of the
network growth literature on the so-called steady-state. This paper takes a
step towards alleviating this gap. We analytically study the degree dynamics of
a given arbitrary network that is subject to growth. We use the theoretical
findings to predict the epidemic properties of the network as a function of
time. We observe that the introduction of new individuals into the network can
enhance or diminish its resilience against endemic outbreaks, and investigate
how this regime shift depends upon the connectivity of newcomers and on how
they establish connections to existing nodes. Throughout, theoretical findings
are corroborated with Monte Carlo simulations over synthetic and real networks.
The results shed light on the effects of network growth on the future epidemic
properties of networks, and offers insights for devising a-priori immunization
strategies.
