Bounding the Size and Probability of Epidemics on Networks

dc.creatorMiller, Joel C.
dc.date2008-03-06
dc.date2008-05-01
dc.date.accessioned2026-07-07T09:36:16Z
dc.date.available2026-07-07T09:36:16Z
dc.descriptionWe consider an infectious disease spreading along the edges of a network which may have significant clustering. The individuals in the population have heterogeneous infectiousness and/or susceptibility. We define the out-transmissibility of a node to be the marginal probability that it would infect a randomly chosen neighbor given its infectiousness and the distribution of susceptibility. For a given distribution of out-transmissibility, we find the conditions which give the upper [or lower] bounds on size and probability of an epidemic, under weak assumptions on the transmission properties, but very general assumptions on the network. We find similar bounds for a given distribution of in-transmissibility (the marginal probability of being infected by a neighbor). We also find conditions giving global upper bounds on size and probability. The distributions leading to these bounds are network-independent. In the special case of networks with high girth (locally tree-like), we are able to prove stronger results. In general the probability and size of epidemics are maximal when the population is homogeneous and minimal when the variance of in- or out-transmissibility is maximal.
dc.descriptionv1 to v2: Minor changes - corrected some typos, clarified some sentences, and added a small number of additional comments. No changes to the scientific content... v2 to v3: added a citation and improved a figure slightly
dc.identifierhttps://arxiv.org/abs/0803.0999
dc.identifierhttp://arxiv.org/abs/0803.0999
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160063
dc.subjectPopulations and Evolution
dc.titleBounding the Size and Probability of Epidemics on Networks
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