Real-time growth rate for general stochastic SIR epidemics on unclustered networks.
Networks have become an important tool for infectious disease epidemiology. Most previous theoretical studies of transmission network models have either considered simple Markovian dynamics at the individual level, or have focused on the invasion threshold and final outcome of the epidemic. Here, we provide a general theory for early real-time behaviour of epidemics on large configuration model networks (i.e. static and locally unclustered), in particular focusing on the computation of the Malthusian parameter that describes the early exponential epidemic growth. Analytical, numerical and Monte-Carlo methods under a wide variety of Markovian and non-Markovian assumptions about the infectivity profile are presented. Numerous examples provide explicit quantification of the impact of the network structure on the temporal dynamics of the spread of infection and provide a benchmark for validating results of large scale simulations.
Warwick Infectious Disease Epidemiology Research Centre (WIDER) and Warwick Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK. Electronic address: l.pellis@warwick.ac.uk.
Lorenzo
L
Pellis
Warwick Infectious Disease Epidemiology Research Centre (WIDER) and Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK.
Simon E F
SE
Spencer
School of Mathematics, University of Manchester, Manchester, M13 9PL, UK; Warwick Infectious Disease Epidemiology Research Centre (WIDER) and Warwick Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK.
Thomas
T
House
D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000635:transmission*; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D008962:Models, Theoretical
Basic reproduction number; Branching process; Configuration model; Epidemic; Malthusian parameter