Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
MC 6486
Demetri Pananos
Department of Applied Mathematics, University of Waterloo
Early Warning Signals of Vaccine Scares
There exists strong evidence that vaccines are extremely effective in the prevention of pediatrics infectious disease, yet despite this evidence, vaccine refusal is still popular some amongst parents. Existing mathematical models of disease and vaccinating dynamics are parsimonious with post scare empirical data, yet lack the ability to predict when a scare will occur. This thesis frames the problem of predicting when a vaccine scare is imminent as a problem in bifurcation theory and critical transitions theory. As a system of differential equations nears a bifurcation point, the system experiences critical slowing down, a loss in resilience to small perturbations from equilibrium. This loss in resilience manifests itself as an increase in the variance and lag-1 autocorrelation of the time series. Using an existing model for vaccinating dynamics, I demonstrate this critical slowing as the system bifurcates from a state of high vaccine coverage to a state of suboptimal vaccine coverage. I also demonstrate that critical slowing can be detected in the population by using the social media site Twitter and Google Trends data. It will be shown that leading to the 2014 measles outbreak in Disneyland, a statistically significant increase in the lag-1 autocorrelation in the time series of tweets with anti-vaccine sentiment is detected. Post outbreak, a statistically significant decrease in the lag-1 autocorrelation is detected, suggesting that population comes sufficiently close to a vaccine scare to elicit outbreaks in those individuals who ceased vaccinating. The results of this thesis provide new tools to monitor vaccine sentiment and maintain vaccine coverage.
Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.