Mathematics of Epidemics on Networks
From Exact to Approximate Models
Page
%P
-
Article
Open AccessNecessary and sufficient conditions for exact closures of epidemic equations on configuration model networks
We prove that it is possible to obtain the exact closure of SIR pairwise epidemic equations on a configuration model network if and only if the degree distribution follows a Poisson, binomial, or negative bino...
-
Article
Open AccessOn Parameter Identifiability in Network-Based Epidemic Models
Modelling epidemics on networks represents an important departure from classical compartmental models which assume random mixing. However, the resulting models are high-dimensional and their analysis is often ...
-
Article
Open AccessThe impact of spatial and social structure on an SIR epidemic on a weighted multilayer network
A key factor in the transmission of infectious diseases is the structure of disease transmitting contacts. In the context of the current COVID-19 pandemic and with some data based on the Hungarian population w...
-
Article
Open AccessEmergent hypernetworks in weakly coupled oscillators
Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triple...
-
Article
Open AccessThe Impact of Contact Structure and Mixing on Control Measures and Disease-Induced Herd Immunity in Epidemic Models: A Mean-Field Model Perspective
The contact structure of a population plays an important role in transmission of infection. Many ‘structured models’ capture aspects of the contact pattern through an underlying network or a mixing matrix. An ...
-
Chapter
Theoretical and Numerical Considerations of the Assumptions Behind Triple Closures in Epidemic Models on Networks
Networks are widely used to model the contact structure within a population and in the resulting models of disease spread. While networks provide a high degree of realism, the analysis of the exact model is ou...
-
Article
Braess’s paradox and programmable behaviour in microfluidic networks
Microfluidic systems are now being designed with precision as miniaturized fluid manipulation devices that can execute increasingly complex tasks. However, their operation often requires numerous external cont...
-
Article
Open AccessEpidemic threshold in pairwise models for clustered networks: closures and fast correlations
The epidemic threshold is probably the most studied quantity in the modelling of epidemics on networks. For a large class of networks and dynamics, it is well studied and understood. However, it is less so for...
-
Article
Localization of current oscillations and synchronization patterns in microchip-based dual electrode flow cell without resistance balancing
The spatiotemporal patterns formed in a two-electrode cell are investigated with oscillatory nickel electrodissolution in a microfluidic flow channel. Because the distances of the two working electrodes to the...
-
Article
Open AccessA monotonic relationship between the variability of the infectious period and final size in pairwise epidemic modelling
For a recently derived pairwise model of network epidemics with non-Markovian recovery, we prove that under some mild technical conditions on the distribution of the infectious periods, smaller variance in the...
-
Chapter and Conference Paper
Map** Structural Diversity in Networks Sharing a Given Degree Distribution and Global Clustering: Adaptive Resolution Grid Search Evolution with Diophantine Equation-Based Mutations
Methods that generate networks sharing a given degree distribution and global clustering can induce changes in structural properties other than that controlled for. Diversity in structural properties, in turn,...
-
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 ...
-
Article
Open AccessConstraints and entropy in a model of network evolution
Barabási–Albert’s “Scale Free” model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real wor...
-
Article
Open AccessDecoding Network Structure in On-Chip Integrated Flow Cells with Synchronization of Electrochemical Oscillators
The analysis of network interactions among dynamical units and the impact of the coupling on self-organized structures is a challenging task with implications in many biological and engineered systems. We expl...
-
Book
-
Chapter and Conference Paper
Variance of Infectious Periods and Reproduction Numbers for Network Epidemics with Non-Markovian Recovery
For a recently derived pairwise model of network epidemics with non-Markovian recovery, we prove that under some mild technical conditions on the distribution of the infectious periods, smaller variance in the...
-
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...
-
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...
-
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...
-
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 ...
