The effects of local spatial structure on epidemiological invasions

Keeling, Matthew James

doi:10.1098/rspb.1999.0716

Cited by 738 publications

(724 citation statements)

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“…The total annual death toll of waterborne diseases is estimated to be 2.8 million people, while diarrhoeal illnesses account for approximately 20 per cent of mortality in children under the age of 5 (Bryce et al 2005). Most of the epidemiological literature has focused on contact networks that are crucial for understanding the evolution of diseases that are directly transmitted from individual to individual or from social group to social group (Diekmann et al 1990;Keeling 1999;Barthelemy et al 2005;Keeling & Eames 2005;Aparicio & Pascual 2007;Colizza & Vespignani 2007). Also, a good deal of work has been done with metapopulation-like models in which the disease is transmitted from patch to patch (Bolker & Grenfell 1996;Brooks et al 2008).…”

Section: Introductionmentioning

confidence: 99%

On spatially explicit models of cholera epidemics

Bertuzzo

Casagrandi

Gatto

et al. 2009

J. R. Soc. Interface.

167

162

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We generalize a recently proposed model for cholera epidemics that accounts for local communities of susceptibles and infectives in a spatially explicit arrangement of nodes linked by networks having different topologies. The vehicle of infection (Vibrio cholerae) is transported through the network links that are thought of as hydrological connections among susceptible communities. The mathematical tools used are borrowed from general schemes of reactive transport on river networks acting as the environmental matrix for the circulation and mixing of waterborne pathogens. Using the diffusion approximation, we analytically derive the speed of propagation for travelling fronts of epidemics on regular lattices (either one-dimensional or two-dimensional) endowed with uniform population density. Power laws are found that relate the propagation speed to the diffusion coefficient and the basic reproduction number. We numerically obtain the related, slower speed of epidemic spreading for more complex, yet realistic river structures such as Peano networks and optimal channel networks. The analysis of the limit case of uniformly distributed population sizes proves instrumental in establishing the overall conditions for the relevance of spatially explicit models. To that extent, the ratio between spreading and disease outbreak time scales proves the crucial parameter. The relevance of our results lies in the major differences potentially arising between the predictions of spatially explicit models and traditional compartmental models of the susceptible -infected -recovered (SIR)-like type. Our results suggest that in many cases of real-life epidemiological interest, time scales of disease dynamics may trigger outbreaks that significantly depart from the predictions of compartmental models.

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Section: Introductionmentioning

confidence: 99%

On spatially explicit models of cholera epidemics

Bertuzzo

Casagrandi

Gatto

et al. 2009

J. R. Soc. Interface.

167

162

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“…For static networks, it is known that spatial structure has an effect on epidemics (see, e.g., [6,7]), and community structure slows down information diffusion due to trapping in dense regions [8][9][10]. There is an intimate relation between inhomogeneous link weights and network topology in social and communication networks [11,12]: Links within communities are strong, while links between them are weak.…”

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confidence: 99%

Small but slow world: How network topology and burstiness slow down spreading

et al. 2011

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While communication networks show the small-world property of short paths, the spreading dynamics in them turns out slow. Here, the time evolution of information propagation is followed through communication networks by using empirical data on contact sequences and the SI model. Introducing null models where event sequences are appropriately shuffled, we are able to distinguish between the contributions of different impeding effects. The slowing down of spreading is found to be caused mainly by weight-topology correlations and the bursty activity patterns of individuals.PACS numbers: 05.45.Tp Most complex physical, biological and social networks show the small-world property, where the average shortest path length is strikingly short when compared to the network size [1]. This means that there is at least one short path between any two nodes, which should give rise to rapid transmission of influence. However, dynamic phenomena on networks [2], such as spreading of pandemics, electronic viruses, and information, follow their own pathways, which are not necessarily topologically efficient [3]. Spreading on real small-world networks turns out to be surprisingly slow, e.g., new infections by a computer virus are reported years after its emergence or the introduction of an anti-virus [4]. Here we aim at resolving this puzzle. For issues such as strategies and timing of vaccinations, improvement of information diffusion, and the slow decay of prevalence of computer viruses, it is crucial to understand the role of the underlying network and temporal activity patterns in the dynamics of spreading.The dynamics of spreading is commonly studied with SI, SIR, or SIS models [5] on static lattices or in mean field, where the dynamics is defined by state changes of individuals between (S)usceptible, (I)nfectious, and (R)ecovered. These models lead to a rapid, exponential growth of prevalence at early stages of spreading, while the dynamics at later stages depend on the model and lattice. For the SI process, the prevalence grows until the whole system reachable from initial conditions is infected, with exponential slowing down towards the end. For the SIR process, competing effects set in and the spreading may remain local or percolate through the system while the SIS process has more complex dynamics.While these results capture some of the qualitative features of real-world processes, the heterogeneity of the systems limits their applicability. First, the interactions of real-world systems span networks by broad distributions of node connections and mesoscopic features in the form of communities with dense internal and sparse external connectivity. Second, interaction intensities vary and are closely coupled to network topology. Third, the daily cycle and bursty character of interaction events give rise to important temporal inhomogeneities.Some aspects of these features have already been studied. For static networks, it is known that spatial structure has an effect on epidemics (see, e.g., [6,7]), and community structure s...

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“…While networks provide a clear departure from classic compartmental models, the role of mean-field models remains crucial. These offer us a reliable way to obtain analytical results, such as epidemic threshold [4,5] and final epidemic size [6], which in turn can be used to uncover the interplay between network properties and dynamic processes on networks.…”

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confidence: 99%