A contact process with a semi-infected state on the complete graph

作者：Xue, Xiaofeng^*

来源：Stochastic Analysis and Applications, 2018, 36(2): 324-340.

DOI：10.1080/07362994.2017.1399802

• Contact process
• semi-infected
• complete graph
• phase transition

In this paper, we are concerned with a contact process with a semi-infected state on the complete graph C-n with n vertices. Our model is a special case of a general model introduced by Schinazi in 2003. In our model, each vertex is in one of three states, namely, healthy, semi-infected, or fully-infected. Only fully-infected vertices can infect others. A healthy vertex becomes semi-infected when being infected while a semi-infected vertex becomes fully-infected when being further infected. Each (semi- and fully-) infected vertex becomes healthy at constant rate. Our main result shows a phase transition for the waiting time until extinction of the fully-infected vertices. Conditioned on all the vertices are fully-infected when t = 0, we show that fully-infected vertices survive for exp{O(n)} units of time when the infection rate > 4 while they die out in O(logn) units of time when < 4.

• 出版日期2018
• 单位北京交通大学