Habitat loss can trigger migration network collapse by isolating migratory bird breeding grounds from nonbreeding grounds. Theoretically, habitat loss can have vastly different impacts depending on the site's importance within the migratory corridor. However, migration‐network connectivity and the impacts of site loss are not completely understood. We used GPS tracking data on 4 bird species in the Asian flyways to construct migration networks and proposed a framework for assessing network connectivity for migratory species. We used a node‐removal process to identify stopover sites with the highest impact on connectivity. In general, migration networks with fewer stopover sites were more vulnerable to habitat loss. Node removal in order from the highest to lowest degree of habitat loss yielded an increase of network resistance similar to random removal. In contrast, resistance increased more rapidly when removing nodes in order from the highest to lowest betweenness value (quantified by the number of shortest paths passing through the specific node). We quantified the risk of migration network collapse and identified crucial sites by first selecting sites with large contributions to network connectivity and then identifying which of those sites were likely to be removed from the network (i.e., sites with habitat loss). Among these crucial sites, 42% were not designated as protected areas. Setting priorities for site protection should account for a site's position in the migration network, rather than only site‐specific characteristics. Our framework for assessing migration‐network connectivity enables site prioritization for conservation of migratory species.

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Although non-Markovian processes are considerably more complicated to analyze, real-world epidemics are likely non-Markovian, because the infection time is not always exponentially distributed. Here, we present analytic expressions of the epidemic threshold in a Weibull and a Gamma SIS epidemic on any network, where the infection time is Weibull, respectively, Gamma, but the recovery time is exponential. The theory is compared with precise simulations. The mean-field non-Markovian epidemic thresholds, both for a Weibull and Gamma infection time, are physically similar and interpreted via the occurrence time of an infection during a healthy period of each node in the graph. Our theory couples the type of a viral item, specified by a shape parameter of the Weibull or Gamma distribution, to its corresponding network-wide endemic spreading power, which is specified by the mean-field non-Markovian epidemic threshold in any network.

Dynamical processes running on different networks behave differently, which makes the reconstruction of the underlying network from dynamical observations possible. However, to what level of detail the network properties can be determined from incomplete measurements of the dynamical process is still an open question. In this paper, we focus on the problem of inferring the properties of the underlying network from the dynamics of a susceptible-infected-susceptible epidemic and we assume that only a time series of the epidemic prevalence, i.e., the average fraction of infected nodes, is given. We find that some of the network metrics, namely those that are sensitive to the epidemic prevalence, can be roughly inferred if the network type is known. A simulated annealing link-rewiring algorithm, called SARA, is proposed to obtain an optimized network whose prevalence is close to the benchmark. The output of the algorithm is applied to classify the network types.

To shed light on the disease localization phenomenon, we study a bursty susceptible-infected-susceptible (SIS) model and analyze the model under the mean-field approximation. In the bursty SIS model, the infected nodes infect all their neighbors periodically, and the near-threshold steady-state prevalence is non-constant and maximized by a factor equal to the largest eigenvalue λ 1 of the adjacency matrix of the network. We show that the maximum near-threshold prevalence of the bursty SIS process on a localized network tends to zero even if λ 1 diverges in the thermodynamic limit, which indicates that the burst of infection cannot turn a localized spreading into a delocalized spreading. Our result is evaluated both on synthetic and real networks.