Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00285-010-0331-2
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dc.titleEffective degree network disease models
dc.contributor.authorLindquist, J.
dc.contributor.authorMa, J.
dc.contributor.authorvan den Driessche, P.
dc.contributor.authorWilleboordse, F.H.
dc.date.accessioned2014-10-16T09:22:25Z
dc.date.available2014-10-16T09:22:25Z
dc.date.issued2011-02
dc.identifier.citationLindquist, J., Ma, J., van den Driessche, P., Willeboordse, F.H. (2011-02). Effective degree network disease models. Journal of Mathematical Biology 62 (2) : 143-164. ScholarBank@NUS Repository. https://doi.org/10.1007/s00285-010-0331-2
dc.identifier.issn03036812
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/96350
dc.description.abstractAn effective degree approach to modeling the spread of infectious diseases on a network is introduced and applied to a disease that confers no immunity (a Susceptible-Infectious-Susceptible model, abbreviated as SIS) and to a disease that confers permanent immunity (a Susceptible-Infectious-Recovered model, abbreviated as SIR). Each model is formulated as a large system of ordinary differential equations that keeps track of the number of susceptible and infectious neighbors of an individual. From numerical simulations, these effective degree models are found to be in excellent agreement with the corresponding stochastic processes of the network on a random graph, in that they capture the initial exponential growth rates, the endemic equilibrium of an invading disease for the SIS model, and the epidemic peak for the SIR model. For each of these effective degree models, a formula for the disease threshold condition is derived. The threshold parameter for the SIS model is shown to be larger than that derived from percolation theory for a model with the same disease and network parameters, and consequently a disease may be able to invade with lower transmission than predicted by percolation theory. For the SIR model, the threshold condition is equal to that predicted by percolation theory. Thus unlike the classical homogeneous mixing disease models, the SIS and SIR effective degree models have different disease threshold conditions. © 2010 Springer-Verlag.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1007/s00285-010-0331-2
dc.sourceScopus
dc.subjectBasic reproduction number
dc.subjectNetwork
dc.subjectSIR disease model
dc.subjectSIS disease model
dc.typeArticle
dc.contributor.departmentPHYSICS
dc.description.doi10.1007/s00285-010-0331-2
dc.description.sourcetitleJournal of Mathematical Biology
dc.description.volume62
dc.description.issue2
dc.description.page143-164
dc.identifier.isiut000286211800001
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