On global and local critical points of extended contact process on homogeneous trees

Duality and complete convergence for multi-type additive growth models

“…Consider the following model introduced in [14], which is somewhat similar to the N -stage contact process considered in Example 4.1. The set of types is {0, 1, ..., N }, with parameters λ, γ and the transitions are…”

“…The term 'growth model' is borrowed from [3], though we work here in continuous rather than discrete time, and with systems that in general may have more than one type of active particle. Examples of additive growth models are the two-stage contact process in [7] and [4], the household model studied in [14], and a spatial analogue of any multi-type branching process (see [10] for an introduction to these processes). On the other hand, the multi-type contact process from [11] is not an additive growth model because it is not additive.…”

“…The term is borrowed from [3], however here we work in continuous rather than discrete time, and with systems having generally more than one type of active particle. Precise definitions are given below, but we note that the class of models considered includes the two-stage contact process [8], [4] the household model studied in [14] and a spatial analogue of any multi-type branching process (see [11] for an introduction to these processes). Since we focus on additive systems, our class of models does not include, for example, the multitype contact process from [12].…”

New Results for the Two-Stage Contact Process

“…More recently, variants of the model have been studied in which there is more than one type of individual [14], [10], or more than one stage of development [9]. In [15] a multitype framework was used to model infection spread between households located at the vertices of a homogenous tree. In [11], a two-stage model of infection spread was studied on scale-free networks.…”