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Traditional mathematical models of epidemic disease had for decadesconventionally considered static structure for contacts. Recently, an upsurgeof theoretical inquiry has strived towards rendering the models more realisticby incorporating the temporal aspects of networks of contacts, societal andonline, that are of interest in the study of epidemics (and other similardiffusion processes). However, temporal dynamics have predominantly focused onlink fluctuations and nodal activities, and less attention has been paid to thegrowth of the underlying network. Many real networks grow: online networks areevidently in constant growth, and societal networks can grow due to migrationflux and reproduction. The effect of network growth on the epidemic propertiesof networks is hitherto unknown---mainly due to the predominant focus of thenetwork growth literature on the so-called steady-state. This paper takes astep towards alleviating this gap. We analytically study the degree dynamics ofa given arbitrary network that is subject to growth. We use the theoreticalfindings to predict the epidemic properties of the network as a function oftime. We observe that the introduction of new individuals into the network canenhance or diminish its resilience against endemic outbreaks, and investigatehow this regime shift depends upon the connectivity of newcomers and on howthey establish connections to existing nodes. Throughout, theoretical findingsare corroborated with Monte Carlo simulations over synthetic and real networks.The results shed light on the effects of network growth on the future epidemicproperties of networks, and offers insights for devising a-priori immunizationstrategies.

Temporal Dynamics of Connectivity and Epidemic Properties of Growing Networks