Who is the infector? General multi-type epidemics and real-time\n susceptibility processes

2018/01/26 by Tom Britton, Britton, Tom, Ka Yin Leung +3
Mathematics · Physics and Astronomy · Psychology · #60K35 #92D30 #COVID-19 epidemiological studies #Complex Network Analysis Techniques #FOS: Mathematics #Mental Health Research Topics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1801.08799

openalex publication_date 2018/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We couple a multi-type stochastic epidemic process with a directed random\ngraph, where edges have random lengths. This random graph representation is\nused to characterise the fractions of individuals infected by the different\ntypes of vertices among all infected individuals in the large population limit.\nFor this characterisation we rely on theory of multi-type real-time branching\nprocesses. We identify a special case of the two-type model, in which the\nfraction of individuals of a certain type infected by individuals of the same\ntype, is maximised among all two-type epidemics approximated by branching\nprocesses with the same mean offspring matrix.\n

Related

• The real-time growth rate of stochastic epidemics on random intersection graphs
• Coupling a branching process to an infinite dimensional epidemic process
• Modelling the spread of two successive SIR epidemics on a configuration model network
• Contagions in Random Networks with Overlapping Communities
• The large graph limit of a stochastic epidemic model on a dynamic\n multilayer network