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Characterizing the Initial Phase of Epidemic Growth on Some Empirical Networks

  • Kristoffer Spricer
  • Pieter Trapman
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 271)

Abstract

A key parameter in models for the spread of infectious diseases is the basic reproduction number \(R_{0}\), which is the expected number of secondary cases a typical infected primary case infects during its infectious period in a large mostly susceptible population. In order for this quantity to be meaningful, the initial expected growth of the number of infectious individuals in the large-population limit should be exponential. We investigate to what extent this assumption is valid by simulating epidemics on empirical networks and by fitting the initial phase of each epidemic to a generalised growth model, allowing for estimating the shape of the growth. For reference, this is repeated on some elementary graphs, for which the early epidemic behaviour is known. We find that for the empirical networks tested in this paper, exponential growth characterizes the early stages of the epidemic, except when the network is restricted by a strong low-dimensional spacial constraint.

Keywords

Epidemics Exponential growth Generalized growth model Reproduction number Stochastic processes 

Notes

Acknowledgements

P.T. was supported by Vetenskapsrådet (Swedish Research Council), project 201604566. The authors would like to thank Tom Britton for valuable discussions.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsStockholm UniversityStockholmSweden

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