TY - JOUR

T1 - Pandemic spread in communities via random graphs

AU - Minzer, Dor

AU - Oz, Yaron

AU - Safra, Muli

AU - Wainstain, Lior

N1 - Publisher Copyright:
© 2021 IOP Publishing Ltd and SISSA Medialab srl.

PY - 2021/11

Y1 - 2021/11

N2 - 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.

AB - 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.

KW - epidemic modelling

KW - networks

KW - random graphs

KW - stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=85120815248&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/ac3415

DO - 10.1088/1742-5468/ac3415

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85120815248

SN - 1742-5468

VL - 2021

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 11

M1 - 113501

ER -