Pandemic spread in communities via random graphs

Dor Minzer, Yaron Oz*, Muli Safra, Lior Wainstain

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Article number113501
Number of pages38
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number11
StatePublished - Nov 2021


FundersFunder number
Horizon 2020 Framework Programme835152


    • epidemic modelling
    • networks
    • random graphs
    • stochastic processes


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