A phase transition in a model for the spread of an infection
A phase transition in a model for the spread of an infection
复制标题
感染传播模型中的相变
DOI：
10.1215/ijm/1258059486
复制
发表时间：
2004
影响因子：
0.6
通讯作者：
V. Sidoravicius
中科院分区：
文献类型：
--
作者：
H. Kesten;V. Sidoravicius
我们证明了一个特定的传染病传播模型在恢复率上有一个相变。模型如下：存在A型和B型的粒子或个体，分别解释为健康和感染。所有粒子都在Z^d上以相同的跳跃率D进行独立的、连续时间的简单随机游动。粒子之间唯一的相互作用是，当一个B粒子跳到一个包含A粒子的位置时，或者反之亦然，A粒子变成了B粒子。所有的B粒子都以λ的速率相互独立地恢复（也就是说，变回A粒子）。我们假设我们以N_A（x，0-）个在x处的A粒子开始系统，并且N_A（x，0-），x在Z^d中是i.i.d.，平均mu_A泊松随机变量。此外，我们从原点处的一个额外的B粒子开始。我们证明了存在一个临界恢复率λ_c > 0，使得当λ\lamda_c满足时，B粒子以正概率存活。
We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B, interpreted as healthy and infected, respectively. All particles perform independent, continuous time, simple random walks on Z^d with the same jump rate D. The only interaction between the particles is that at the moment when a B-particle jumps to a site which contains an A-particle, or vice versa, the A-particle turns into a B-particle. All B-particles recuperate (that is, turn back into A-particles) independently of each other at a rate lamda. We assume that we start the system with N_A(x,0-) A-particles at x, and that the N_A(x,0-), x in Z^d, are i.i.d., mean mu_A Poisson random variables. In addition we start with one additional B-particle at the origin. We show that there is a critical recuperation rate lambda_c > 0 such that the B-particles survive (globally) with positive probability if lambda \lamda_c.