A contact process with a semi-infected state on the complete graph. Issue 2 (4th March 2018)

• Record Type: Journal Article
• Authors: Xue, Xiaofeng
• Is Part Of: Stochastic analysis and applications. Volume 36:Issue 2(2018)
• Page Start: 324
• Page End: 340
• Publication Date: 2018-03-04
• Subjects: Contact process -- semi-infected -- complete graph -- phase transition; 60K35; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2017.1399802
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: In this paper, we are concerned with a contact process with a semi-infected state on the complete graph Cn 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 λ > 4 while they die out in O (log n ) units of time when λ < 4.