Edge-based network disease models, in comparison to classic compartmental epidemiological models, better capture social factors affecting disease spread such as contact duration and social heterogeneity. We reason that there should exist infinitely many equilibria rather than only an endemic equilibrium and a disease-free equilibrium for the edge-based network disease model commonly used in the literature, as there do not exist any changes in demographic in the model. We modify the commonly used network model by relaxing some assumed conditions and factor in a dependency on initial conditions. We find that this modification still accounts for realistic dynamics of disease spread (such as the probability of contracting a disease based off your neighbors' susceptibility to the disease) based on the basic reproduction number. Specifically, if the basic reproduction number is below 1, then the infection dies out; while if the basic reproduction number is above 1, then there is possibility of an epidemic.
Bachelor of Science (B.S.)
College of Sciences
Mai, Sabrina, "Rigorous Analysis of an Edge-Based Network Disease Model" (2019). Honors Undergraduate Theses. 537.