  In this paper, we aim to understand the transient dynamics of a
susceptible-infected (SI) epidemic spreading process on a large network. The SI
model has been largely overlooked in the literature, while it is naturally a
better fit for modeling the malware propagation in early times when
patches/vaccines are not available, or over a wider range of timescales when
massive patching is practically infeasible. Nonetheless, its analysis is simply
non-trivial, as its important dynamics are all transient and the usual
stability/steady-state analysis no longer applies. To this end, we develop a
theoretical framework that allows us to obtain an accurate closed-form
approximate solution to the original SI dynamics on any arbitrary network,
which captures the temporal dynamics over all time and is tighter than the
existing approximation, and also to provide a new interpretation via
reliability theory. As its applications, we further develop vaccination
policies with or without knowledge of already-infected nodes, to mitigate the
future epidemic spreading to the extent possible, and demonstrate their
effectiveness through numerical simulations.

Social and Information Networks;Physics and Society