Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Characterizing the Initial Phase of Epidemic Growth on some Empirical Networks
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0003-0233-0022
Stockholm University, Faculty of Science, Department of Mathematics.
2017 (English)Manuscript (preprint) (Other academic)
Abstract [en]

A key parameter in models for the spread of infectious diseases is the basic reproduction number R0, 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 performing repeated simulations of epidemics on selected empirical networks, viewing each epidemic as a random process in discrete time. The initial phase of each epidemic is analyzed by fitting the number of infected people at each time step to a generalised growth model, allowing for estimating the shape of the growth. For reference, similar investigations are done on some elementary graphs such as integer lattices in different dimensions and configuration model 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, such as is the case for the two-dimensional square lattice. However, on finite integer lattices of sufficiently high dimension, the early development of epidemics shows exponential growth.

Place, publisher, year, edition, pages
2017.
Keywords [en]
Epidemics, Exponential growth, Generalized growth model, Reproduction number, Stochastic processes
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-154927OAI: oai:DiVA.org:su-154927DiVA, id: diva2:1195903
Conference
Stochastic Processes and Algebraic Structures – From Theory Towards Applications" (SPAS2017), Västerås – Stockholm, 2017
Funder
Swedish Research Council, 2016-04566Available from: 2018-04-06 Created: 2018-04-06 Last updated: 2018-04-13
In thesis
1. Random networks with weights and directions, and epidemics thereon
Open this publication in new window or tab >>Random networks with weights and directions, and epidemics thereon
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Networks, consisting of nodes and of edges, can be used to model numerous phenomena, e.g, web pages linking to each other or interactions between people in a population. Edges can be directed, such as a one way link from one web page to another, or undirected (bi-directional), such as physical contacts between pairs of people, which potentially could spread an infection either way between them. Edges can also have weights associated with them, in this thesis corresponding to the probability that an infection is transmitted on the edge.

Empirical networks are often only partially known, in the form of ego-centric network data where only a subset of the nodes and the number of adjacent edges of each node have been observed. This situation lends itself well to analysis through the undirected or partially directed configuration model - a random network model where the number of edges of each node (the degree) is given but where the way these edges are connected is random.

The four papers in this thesis are concerned with the properties of the configuration model and with the usefulness of it with respect to its ability to model the spread of epidemics on empirical networks. Paper I proves the asymptotic convergence to a given degree distribution for the partially directed configuration model. In Paper II it is shown that epidemics on some empirical and theoretically constructed networks grow exponentially, similarly to what can be seen on the corresponding configuration models. Finally, in Papers III and IV, large population analytical results for the reproduction number, the probability of a large epidemic outbreak and the final size of such an outbreak are derived assuming a configuration model network with weighted and/or partially directed edges. These results are then evaluated on several large empirical networks upon which epidemics are simulated. We find that on some of these networks the analytical expressions are compatible with the results of the simulations. This makes the model useful as a tool for analyzing such networks.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2018. p. 28
Keywords
Epidemics, Reproduction number, Final size, Large outbreak, Weighted network, Undirected, Partially directed, Configuration model, Copula
National Category
Probability Theory and Statistics Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-154930 (URN)978-91-7797-278-5 (ISBN)978-91-7797-279-2 (ISBN)
Public defence
2018-05-31, Sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 14:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 2009-5759Riksbankens Jubileumsfond, P12-0705:1Swedish Research Council, 2016-04566Swedish Research Council, 2015-05015
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 3: Manuscript. Paper 4: Manuscript.

Available from: 2018-05-07 Created: 2018-04-12 Last updated: 2018-05-04Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

arXiv:1709.00973

Search in DiVA

By author/editor
Spricer, KristofferTrapman, Pieter
By organisation
Department of Mathematics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 2 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf