Pandemic spread in communities via random graphs
Name
Minzer_2021_J._Stat._Mech._2021_113501.pdf
Description
Published version
Size
1.48 MB
Format
Adobe PDF
Checksum (MD5)
9364b4430c5333a9dd7f9647481e1513
Author(s)
Minzer, Dor
Oz, Yaron
Safra, Muli
Wainstain, Lior
Date Issued
2021
Journal
Journal of Statistical Mechanics: Theory and Experiment
Publisher
IOP Publishing
Citation
Minzer, Dor, Oz, Yaron, Safra, Muli and Wainstain, Lior. 2021. "Pandemic spread in communities via random graphs." Journal of Statistical Mechanics: Theory and Experiment, 2021 (11).
Version
Final published version
Abstract
Abstract
Working in the multi-type Galton–Watson branching-process framework we analyse the spread of a pandemic via a general multi-type random contact graph. Our model consists of several communities, and takes, as input, parameters that outline the contacts between individuals in distinct communities. Given these parameters, we determine whether there will be an outbreak and if yes, we calculate the size of the giant-connected-component of the graph, thereby, determining the fraction of the population of each type that would be infected before it ends. We show that the pandemic spread has a natural evolution direction given by the Perron–Frobenius eigenvector of a matrix whose entries encode the average number of individuals of one type expected to be infected by an individual of another type. The corresponding eigenvalue is the basic reproduction number of the pandemic. We perform numerical simulations that compare homogeneous and heterogeneous spread graphs and quantify the difference between them. We elaborate on the difference between herd immunity and the end of the pandemic and the effect of countermeasures on the fraction of infected population.
Working in the multi-type Galton–Watson branching-process framework we analyse the spread of a pandemic via a general multi-type random contact graph. Our model consists of several communities, and takes, as input, parameters that outline the contacts between individuals in distinct communities. Given these parameters, we determine whether there will be an outbreak and if yes, we calculate the size of the giant-connected-component of the graph, thereby, determining the fraction of the population of each type that would be infected before it ends. We show that the pandemic spread has a natural evolution direction given by the Perron–Frobenius eigenvector of a matrix whose entries encode the average number of individuals of one type expected to be infected by an individual of another type. The corresponding eigenvalue is the basic reproduction number of the pandemic. We perform numerical simulations that compare homogeneous and heterogeneous spread graphs and quantify the difference between them. We elaborate on the difference between herd immunity and the end of the pandemic and the effect of countermeasures on the fraction of infected population.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1088/1742-5468/AC3415
