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During an epidemic, infectious individuals might not be detectable until sometime after becoming infected. The studies show that carriers with mild or nosymptoms are the main contributors to the transmission of a virus within thepopulation. The average time it takes to develop the symptoms causes a delay inthe spread dynamics of the disease. When considering the influence of delay onthe disease propagation in epidemic networks, depending on the value of thetime-delay and the network topology, the peak of epidemic could be considerablydifferent in time, duration, and intensity. Motivated by the recent worldwideoutbreak of the COVID-19 virus and the topological extent in which this virushas spread over the course of a few months, this study aims to highlight theeffect of time-delay in the progress of such infectious diseases in themeta-population networks rather than individuals or a single population. Inthis regard, the notions of epidemic network centrality in terms of theunderlying interaction graph of the network, structure of the uncertainties,and symptom development duration are investigated to establish acentrality-based analysis of the disease evolution. A convex traffic volumeoptimization method is then developed to control the outbreak. The controlprocess is done by identifying the sub-populations with the highest centralityand then isolating them while maintaining the same overall traffic volume(motivated by economic considerations) in the meta-population level. Thenumerical results, along with the theoretical expectations, highlight theimpact of time-delay as well as the importance of considering the worst-casescenarios in investigating the most effective methods of epidemic containment.

Centrality-Based Traffic Restriction in Delayed Epidemic Networks