Metastable localization of diseases in complex networks

Abstract

We describe the phenomenon of localization in the epidemic susceptible-infective-susceptible model on highly heterogeneous networks in which strongly connected nodes (hubs) play the role of centers of localization. We find that in this model the localized states below the epidemic threshold are metastable. The longevity and scale of the metastable outbreaks do not show a sharp localization transition; instead there is a smooth crossover from localized to delocalized states as we approach the epidemic threshold from below. Analyzing these long-lasting local outbreaks for a random regular graph with a hub, we show how this localization can be detected from the shape of the distribution of the number of infective nodes.

Vacuum instabilities in the N2HDM

“…For the purpose of studying the interplay between different possible vacua, it is convenient to introduce a bilinear formalism, similar to that which has been developed for the 2HDM [8-10, 14, 15, 26-34]. This formalism has been applied to models with different scalar content, for instance the 3HDM [35,36] or the complex singlet-doublet model [37]. For the N2HDM let us define five real quantities,…”

“…These results underline the curiously unique nature of the vacuum structure in the 2HDM, where the existence of a minimum of a given nature automatically implies that no minima of different types may exist. That property is not shared by models with a different scalar content -even in models with a simpler scalar content, such as the doublet + singlet (real or complex) model, the vacuum structure is much more complex, and no general, 2HDM-like conclusions may be drawn [37]. In models with more than two doublets the 2HDM stability also breaks down, at least concerning charge breaking [38].…”

Network Localization Is Unalterable by Infections in Bursts

“…is not necessarily finite. In the following part, we first clarify some misconceptions about the SIS localization in previous studies and show the availability of mean-field methods [6], [7], [14], [15]. We point out that the order of the near-threshold prevalence as a function of the network size N is essential for understanding the influence of the network structure on spreading processes.…”

“…Ferreira et al [7] argue that if a finite number of nodes are infected using mean-field theory, then the virus eventually dies out and then the mean-field approximations [4], [14] fail due to their omission of the absorbing state.…”

Stability of neutral minima against charge breaking in the Higgs triplet model

“…Since the potential only has quadratic and quartic terms when µ = 0, and we are interested in comparing the value of the potential at different extrema, it is tempting to attempt to use a bilinear formalism similar to the one employed for the 2HDM [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Generalisations of this formalism have been used to study the vacuum structure of models other than the SM, for instance the 3HDM [36,37], the complex singlet-doublet model [38] or the N2HDM [39]. We recall that in those works the bilinears defined are always real gauge-invariant quantities, quadratic in the fields.…”