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To shed light on the disease localization phenomenon, we study a burstysusceptible-infected-susceptible (SIS) model and analyze the model under themean-field approximation. In the bursty SIS model, the infected nodes infectall their neighbors periodically, and the near-threshold steady-stateprevalence is non-constant and maximized by a factor equal to the largesteigenvalue $\lambda_1$ of the adjacency matrix of the network. We show that themaximum near-threshold prevalence of the bursty SIS process on a localizednetwork tends to zero even if $\lambda_1$ diverges in the thermodynamic limit,which indicates that the burst of infection cannot turn a localized spreadinginto a delocalized spreading. Our result is evaluated both on synthetic andreal networks.

Network localization is unalterable by infections in bursts