RESUMO
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.
Assuntos
Epidemias/estatística & dados numéricos , Modelos Estatísticos , Surtos de Doenças/estatística & dados numéricos , Transmissão de Doença Infecciosa/estatística & dados numéricos , Humanos , Fatores de TempoRESUMO
The secretory cycle of hypopharyngeal glands (HPGs) in Scaptotrigona postica resembles that of Apis mellifera: in newly emerged workers the HPGs are in prefunctional state, their maximum development happens in the nurse workers and in forager workers they show signs of reabsorption. In S. postica these glands are also present in queens and males where they are more developed in newly emerged individuals. The ultrastructural features of the HPG secretory cycle in workers of S. postica and A. mellifera are alike: granular endoplasmic reticulum well developed, large secretion masses around the intracellular canaliculus in nurse workers and extensive degenerative structures in forager workers. Then it is suggested that the HPG secrete similar substances in both species. A second secretory cycle seems to occur in early foragers, may be with production of enzymes. The role of the HPGs in queens and males remains unknown but one possibility is enzyme production.
Assuntos
Abelhas/ultraestrutura , Animais , Abelhas/metabolismo , Feminino , Hipofaringe/metabolismo , Hipofaringe/ultraestrutura , MasculinoRESUMO
The secretory cycle of hypopharyngeal glands (HPGs) in Scaptotrigona postica resembles that of Apis mellifera: in newly emerged workers the HPGs are in prefunctional state, their maximum development happens in the nurse workers and in forager workers they show signs of reabsorption. In S. postica these glands are also present in queens and males where they are more developed in newly emerged individuals. The ultrastructural features of the HPG secretory cycle in workers of S. postica and A. mellifera are alike: granular endoplasmic reticulum well developed, large secretion masses around the intracellular canaliculus in nurse workers and extensive degenerative structures in forager workers. Then it is suggested that the HPG secrete similar substances in both species. A second secretory cycle seems to occur in early foragers, may be with production of enzymes. The role of the HPGs in queens and males remains unknown but one possibility is enzyme production.