Immunization of Geographical Networks

Random mobility and the spread of infection

“…Hence, using a well-known result about the expectation of the maximum of i.i.d. exponentials, we obtain lE[ T1] = 0 C�;��)) = O(g(n) logg(n)), (2) where Hk � L� = l i -1 = O( log k) is the kth harmonic number. Also, by a union bound over the tails of g(n) i.i.…”

“…There has been much work in studying the static spread of infection/innovation using various notions of influence and susceptibility, both numerically using field data/extensive simulations [8], [3], [4], [5] and analytically [9], [14], [15], [16]. For the case of spreading with virtual mobility, many numerical studies have investigated the spread of infectious diseases with specific mobility patterns, e. g. via airline networks [23], heterogeneous geographic means [1], [2], and recently, electronic pathways [21], [17], [18], [19], [20]. Several notable works in com munication engineering include studies in which all network nodes are simultaneously physically mobile -for designing gossip algorithms [13], [6] and improving the capacity of wireless networks [12] -and analyses of rumour spreading on fully-connected graphs [10], [11].…”

“…Rumours and news stories propagate among people linked by various means of communication, diseases diffuse as epidemics through populations by various modes, plants disperse pollen/seeds and thus genetic traits geographi cally, riots spread across pockets of communities, advertisers aim to disseminate information about goods through net works of consumers, and computer viruses, email worms and software patches piggy-back across computer networks. Un derstanding how infection/information/innovation can travel across networks has been a subject of extensive study in disciplines ranging from epidemiology [1], [2], sociology [3], [4] and computer science [5], [6], [7] to physics [8], information theory/networking [9], [10], [11], [12], [13] and applied mathematics [14], [15], [16], yielding valuable insights into qualitative and quantitative aspects of network spread behaviour.…”

Epidemic thresholds with external agents

“…The role of external sources in epidemic spread has been studied under different models. In the context of human disease spread, works include [17] (airline effects), [18] (geographic effects) and [19] (multiscale effects). This is paralleled by studies of epidemics on computer/mobile phone networks [20], [21], [22].…”