  During an epidemic, infectious individuals might not be detectable until some
time after becoming infected. The studies show that carriers with mild or no
symptoms are the main contributors to the transmission of a virus within the
population. The average time it takes to develop the symptoms causes a delay in
the spread dynamics of the disease. When considering the influence of delay on
the disease propagation in epidemic networks, depending on the value of the
time-delay and the network topology, the peak of epidemic could be considerably
different in time, duration, and intensity. Motivated by the recent worldwide
outbreak of the COVID-19 virus and the topological extent in which this virus
has spread over the course of a few months, this study aims to highlight the
effect of time-delay in the progress of such infectious diseases in the
meta-population networks rather than individuals or a single population. In
this regard, the notions of epidemic network centrality in terms of the
underlying interaction graph of the network, structure of the uncertainties,
and symptom development duration are investigated to establish a
centrality-based analysis of the disease evolution. A convex traffic volume
optimization method is then developed to control the outbreak. The control
process is done by identifying the sub-populations with the highest centrality
and then isolating them while maintaining the same overall traffic volume
(motivated by economic considerations) in the meta-population level. The
numerical results, along with the theoretical expectations, highlight the
impact of time-delay as well as the importance of considering the worst-case
scenarios in investigating the most effective methods of epidemic containment.
