SIR epidemics and vaccination on random graphs with clustering

Autor: Carolina Fransson, Pieter Trapman
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Poisson distribution
01 natural sciences
Quantitative Biology::Other
Communicable Diseases
Models
Biological
Article
Clustering
010305 fluids & plasmas
Disease Outbreaks
03 medical and health sciences
symbols.namesake
0103 physical sciences
FOS: Mathematics
Computer Graphics
Quantitative Biology::Populations and Evolution
Cluster Analysis
Humans
Computer Simulation
Configuration model
Cluster analysis
030304 developmental biology
Mathematics
Branching process
Discrete mathematics
Random graph
0303 health sciences
Applied Mathematics
Probability (math.PR)
Vaccination
Numerical Analysis
Computer-Assisted
Computer Science::Social and Information Networks
Models
Theoretical
Agricultural and Biological Sciences (miscellaneous)
Outcome (probability)
Branching processes
Modeling and Simulation
symbols
SIR epidemics
Graph (abstract data type)
Disease Susceptibility
Epidemic model
Basic reproduction number
Mathematics - Probability
Zdroj: Journal of Mathematical Biology
ISSN: 1432-1416
0303-6812
Popis: In this paper we consider Susceptible \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document}→ Infectious \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document}→ Recovered (SIR) epidemics on random graphs with clustering. To incorporate group structure of the underlying social network, we use a generalized version of the configuration model in which each node is a member of a specified number of triangles. SIR epidemics on this type of graph have earlier been investigated under the assumption of homogeneous infectivity and also under the assumption of Poisson transmission and recovery rates. We extend known results from literature by relaxing the assumption of homogeneous infectivity both in individual infectivity and between different kinds of neighbours. An important special case of the epidemic model analysed in this paper is epidemics in continuous time with arbitrary infectious period distribution. We use branching process approximations of the spread of the disease to provide expressions for the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0, the probability of a major outbreak and the expected final size. In addition, the impact of random vaccination with a perfect vaccine on the final outcome of the epidemic is investigated. We find that, for this particular model, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0 equals the perfect vaccine-associated reproduction number. Generalizations to groups larger than three are discussed briefly.
Databáze: OpenAIRE
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