Stability and Robustness Analysis of Epidemic Networks with Multiple Time-Delays

Several sources of delay in an epidemic network might negatively affect the stability and robustness of the entire network. In this paper, a multi-delayed Susceptible-Infectious-Susceptible (SIS) model is applied on a metapopulation network, where the epidemic delays are categorized into local and global delays. While local delays result from intra-population lags such as symptom development duration or recovery period, global delays stem from inter-population lags, e.g., transition duration between subpopulations. The theoretical results for a network of subpopulations with identical linear SIS dynamics and different types of time-delay show that depending on the type of time-delay in the network, different eigenvalues of the underlying graph should be evaluated to obtain the feasible regions of stability. The delay-dependent stability of such epidemic networks has been analytically derived, which eliminates potentially expensive computations required by current algorithms. The effect of time-delay on the H
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norm-based performance of a class of epidemic networks with additive noise inputs and multiple delays is studied and the closed form of their performance measure is derived using the solution of delayed Lyapunov equations. As a case study, the theoretical findings are implemented on a network of United States’ busiest airports.