Grant: Discovery Grants Program - Individual

The program will develop global dynamics and bifurcation theories/technologies, with applications to prediction of long-term patterns of zoonotic disease spread to inform outbreak preparedness and response.  The program will involve several themes ranging from fundamental research to novel applications. The fundamental research will fill the lack of a much-needed comprehensive theory to understand mechanisms of recurrent/oscillatory behaviors of biological (including epidemiological) systems involving predation. The fundamental research about the long-term behaviors for systems preserving "orders" with respect to high rank "cones" will be a major advance from the celebrated theory of monotone dynamical systems (applicable only to cooperative and some competitive interactions), to predator-prey interaction and disease transmission. The fundamental research is motivated by and will be applied to important issues arising from zoonotic disease and ecosystem management, and neural differential equation architecture design for data informatics. We will 1). Construct novel high rank "cones" and establish order-preserving properties of general classes of (ordinary and partial) delay differential equations (DDEs) with respect to these "cones". The novelty includes the use of Razumikhin techniques and Lyapunov-type functions, and the extension of the quasi-monotonicity condition. Extending the global dynamics theory of DDEs with positive feedback to other nonlinear systems with negative and mixed feedbacks will be significant. 2). Formulate novel classes of epidemic systems incorporating behavioural adaptation of (human, vector, host) individuals to the real or perceived risks of infections and population survivals, and describe emerging patterns of zoonotic disease transmission and population dynamics. In addition to the novelty of the formulated models, our approach will lead to novel dynamic bifurcation and generic periodicity techniques inspired by and applied to specific systems and discover new and complex dynamic patterns resulted from the time-lag and nonlinear behavioral adaptations. This will be significant for it provides insights on mechanisms of multiple waves of disease outbreaks and suggest optimal public health interventions. 3). Develop neural differential equation frameworks which infer, from evolving data and knowledge of emerging disease epidemiology, approximating analytic expressions of hidden mechanisms impacting disease transmission. The novelty includes techniques to analyze the global bifurcations of DDEs with nonlinear terms and delay distributions that can only be approximated from data by deep learning neural networks. This is significant in integrating deep learning and dynamical system theory to provide scenario analyses.  The program will engage international collaborative networks, involve governmental and industrial organizations, and foster an interdisciplinary collaboration environment for trainees at all levels.