title: On global and local critical points of extended contact process on homogeneous trees.
abstract: We study spatial stochastic epidemic models called households models. The households models have more than two states at each vertex of a graph in contrast to the contact process. We show that, in the households models on trees, two thresholds of infection rates characterize epidemics. The global critical infection rate is defined by epidemic occurrence. However, some households may be eventually disease-free even for infection rates above the global critical infection rate, in as far as they are smaller than the local critical point. Whether the global one is smaller than the local one depends on the graph and the model. We show that, in the households models, the global one is smaller than the local one on homogeneous trees.
authors.affiliation: Aihara Complexity Modelling Project, ERATO, JST, 3-23-5-201 Uehara, Shibuya-ku, Tokyo 151-0064, Japan. sugimine@aihara.jst.go.jp
authors.forename: Nobuaki
authors.initials: N
authors.lastname: Sugimine
authors.forename: Naoki
authors.initials: N
authors.lastname: Masuda
authors.forename: Norio
authors.initials: N
authors.lastname: Konno
authors.forename: Kazuyuki
authors.initials: K
authors.lastname: Aihara
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology*; D004196:Disease Outbreaks; D004812:Epidemiologic Methods; D005191:Family Characteristics; D006801:Humans; D015233:Models, Statistical; D013269:Stochastic Processes