Physical Sciences and Mathematics Commons^™

Modeling The Heterogeneous Temporal Dynamics Of Epidemics On Networks, Andrea Joan Allen

Graduate College Dissertations and Theses

Mathematical models of infectious disease are important tools for understanding large-scale patterns of how a disease spreads through a population. Predictions of trends from disease models help guide public health prevention and mitigation measures. Most simple disease models assume that the population is randomly mixed, but real-world populations exhibit heterogeneous patterns in the way people interact. These differences in population structure can be represented by networks. Networks can then be incorporated into disease models by using various interdisciplinary concepts and tools. Yet even network disease models often overlook that populations change over time. In this thesis, two models of infectious …

On The Dynamics And Structure Of Multiple Strain Epidemic Models And Genotype Networks, Blake Joseph Mitchell Williams

Graduate College Dissertations and Theses

Mathematical disease modeling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modeling community to focus on the complexity of other factors such as contact structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics.

This body of work first explores the role of strain-transcending immunity in mathematical disease models, …