14 Result(s)
within
Chapter
Joel C. Miller
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Chapter and Conference Paper
Fast Variables Determine the Epidemic Threshold in the Pairwise Model with an Improved Closure
Pairwise models are widely used to model epidemic spread on networks. This includes the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact ...
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Chapter
Disease spread in networks with large-scale structure
This book has developed analytic models of disease spread on networks. All of our tractable models require closure assumptions. The closure process assumes that we can explain the dynamics at the network scale...
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Chapter
Introduction to networks and diseases
Mathematical models are caricatures of real systems that aim to capture the fundamental mechanisms of some process in order to explain observations or predict outcomes. No model — no matter how complicated — i...
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Chapter
Propagation models on networks: bottom-up
In this chapter, we present a different approach to deriving exact models. In Chapter 2, we began with equations for every possible state of the system and then aggregated them into a simpler form. Here, we be...
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Chapter
Mean-field approximations for heterogeneous networks
Section 4.5 showed that the homogeneous mean-field approximations cannot capture the system behaviour for networks with heterogeneous degree distributions. The heterogeneity in degree can significantly affect ...
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Chapter
Hierarchies of SIR models
This chapter focuses on the relationships between the continuous-time SIR models we have previously derived and identifying conditions under which they are appropriate. Unless otherwise noted, the models discu...
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Chapter
Non-Markovian epidemics
Early studies of non-Markovian epidemics focused on SIR dynamics on fully connected networks, or homogeneously mixing populations, with the infection process being Markovian but with the infectious period take...
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Chapter
Exact propagation models on networks: top down
Chapter 1 introduced SIS and SIR diseases and some weaknesses of compartmental models that can be remedied by considering networks. In this chapter, we begin our n...
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Chapter
Mean-field approximations for homogeneous networks
As seen in Chapters 2 and 3, because of the high-dimensionality of exact mathematical models describing spreading processes on networks, the models are often neither tractable nor numerically solvable for n...
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Chapter
PDE limits for large networks
In previous chapters, it was shown that dynamics on networks can be described by continuous-time Markov chains, where probabilities of states are determined by master equations. While limiting mean-field ODE m...
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Chapter
Percolation-based approaches for disease modelling
The methods introduced thus far are applicable to both SIS and SIR diseases. This chapter focuses primarily on SIR disease. Once a node u becomes infected with an SIR disease, no other node affects the timing of ...
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Chapter
Dynamic and adaptive networks
An important feature of many real-world networks is the transient nature of some interactions. Thus far, our models have explicitly assumed that the network is static. That is, we assume that the rate of partn...
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Chapter
Map** Out Emerging Network Structures in Dynamic Network Models Coupled with Epidemics
We consider the susceptible – infected – susceptible (SIS) epidemic on a dynamic network model with addition and deletion of links depending on node status. We analyse the resulting pairwise model using classi...
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Chapter and Conference Paper
Efficient Generation of Networks with Given Expected Degrees
We present an efficient algorithm to generate random graphs with a given sequence of expected degrees. Existing algorithms run in $\mathcal{O}...
