Who is the infector? General multi-type epidemics and real-time susceptibility processes. (June 2019)

• Record Type: Journal Article
• Authors: Britton, Tom; Leung, Ka Yin; Trapman, Pieter
• Is Part Of: Advances in applied probability. Volume 51:Number 2(2019)
• Page Start: 606
• Page End: 631
• Publication Date: 2019-06
• Subjects: Epidemics, -- multi-type branching process approximation, -- susceptibility process, -- directed random graph; Primary 92D30, -- 60K35, -- Secondary 05C80, -- 60J80; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2019.25
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: We couple a multi-type stochastic epidemic process with a directed random graph, where edges have random weights (traversal times). This random graph representation is used to characterise the fractions of individuals infected by the different types of vertices among all infected individuals in the large population limit. For this characterisation, we rely on the theory of multi-type real-time branching processes. We identify a special case of the two-type model in which the fraction of individuals of a certain type infected by individuals of the same type is maximised among all two-type epidemics approximated by branching processes with the same mean offspring matrix.