Network Models of Epidemics
Date
2024-01-29
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
Type
Thesis
Degree Level
Masters
Abstract
This thesis investigates mathematical models of disease spread centering on the SIR (Susceptible-Infected-Recovered) model within diverse network frameworks. The study begins with a detailed exploration of the
deterministic compartmental SIR model proposed by Kermack and McKendrick (1927), where key quantities
such as the basic reproduction number and epidemic size are scrutinized. The research then addresses the
limitations of deterministic models, particularly their assumption of homogeneous mixing by exploring Continuous Time Markov Chain (CTMC) models in network contexts. An example on a 3-node network is solved
using Dolgov et al. and McCulloch et al.’s approaches. To investigate disease dynamics on larger networks,
we apply the methodology proposed by Mark Newman (2000) that combines percolation theory with the
configuration network model. This approach is particularly well-suited for analyzing complex network structures in epidemiological studies and allows us to examine key network properties using generating function
approaches. We focus on random network models such as the Erdős-Rényi (ER) and Barabási-Albert (BA)
models to apply the configuration model and study SIR dynamics on these networks. Comparing the spread
of the infection in these networks, we emphasize the role of hubs (most connected nodes) in the BA network.
Edge removal processes are also explored to model mitigation strategies and measure their effect on disease
spread. To understand the impact of lockdown measures on disease transmission, we apply network models
for a data-set from Pakistan considered in the reference Rafiq et al. and we also extend our analysis to
capture lockdown scenarios that take into account complex network social structures such as those studied
by Maheshwari et al.. Overall, this thesis highlights the importance of network structure in disease transmission and emphasizes the need for more sophisticated models to accurately reflect the complexities of real-life
individual interactions in epidemics.
Description
Keywords
Network, SIR Model.
Citation
Degree
Master of Science (M.Sc.)
Department
Mathematics and Statistics
Program
Statistics