Network Models of Epidemics
| dc.contributor.advisor | Srinivasan, Raj | |
| dc.contributor.advisor | Soteros, Chris | |
| dc.contributor.committeeMember | Soteros, Chris | |
| dc.contributor.committeeMember | Liu, Juxin | |
| dc.contributor.committeeMember | Li, Longhai | |
| dc.creator | Barua, Yaindrila | |
| dc.date.accessioned | 2024-01-29T16:13:44Z | |
| dc.date.available | 2024-01-29T16:13:44Z | |
| dc.date.copyright | 2024 | |
| dc.date.created | 2024-01 | |
| dc.date.issued | 2024-01-29 | |
| dc.date.submitted | January 2024 | |
| dc.date.updated | 2024-01-29T16:13:45Z | |
| dc.description.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. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | https://hdl.handle.net/10388/15467 | |
| dc.language.iso | en | |
| dc.subject | Network | |
| dc.subject | SIR Model. | |
| dc.title | Network Models of Epidemics | |
| dc.type | Thesis | |
| dc.type.material | text | |
| thesis.degree.department | Mathematics and Statistics | |
| thesis.degree.discipline | Statistics | |
| thesis.degree.grantor | University of Saskatchewan | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science (M.Sc.) |