Tom Bury, Applied Mathematics, University of Waterloo
Critical Transitions and Endogenisation in Coupled Behaviour-Disease Systems
Gradual variation in external conditions over time may invoke abrupt changes in nature and society. Such phenomena are known as ‘critical transitions’ and are of great interest due to their diverse scope and profound consequences. Despite huge advances in the theory of dynamical systems, critical transitions remain difficult to predict due to the complexity of nature itself. Recent literature, however, suggests generic early-warning signals that may allow us to prevent unwanted transitions.
This seminar focuses on a coupled behaviour-disease model at the population level, with the aim of better understanding parental vaccination decisions in the face of epidemics, vaccination risks and social norms. Recent decline in vaccination coverage of certain developed countries has triggered measles epidemics. As for the recent California outbreak, vaccination coverage responded quickly as parents became incentivised to vaccinate their child. Countries such as France however, have remained at low immunisation rates and suffered regular measles epidemics. We aim to characterise and explain such outcomes through use of critical transition theory. Endogenisation of the control parameter and alternate mechanisms for the model are discussed as motive for future research.