Mathematical Analysis and Statistical Inference of Complex Dynamical Systems

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The objectives of the proposed research are: (1) to develop new mathematical theories and analytic tools for the investigation of large--scale and complex dynamical systems arising from many fields of science and engineering, using a mathematical framework of interconnected systems of nonlinear differential equations defined over a network represented by a directed graph; and (2) to develop a rigorous mathematical modelling approach to public health assessment.***The research will address significant challenges regarding both theoretic and practical aspects of complex and large--scale dynamical systems such as:***- How do interconnected simple vertex systems give rise to complex system behaviours?***- How to classify and describe mathematically different types of complex system behaviours?***- How does each type of system behaviours correlate to the network topology of geometry?***- How does complexity in an interconnected system influence its stability?***- Develop realistic mathematical models to investigate the complex temporal and spatial dynamics of the infectious diseases at different scales;***- Develop a rigorous theoretical approach that integrate mathematical models, disease surveillance data, and methodologies of statistical inference to analyze past disease data, assess past disease dynamics, and evaluate the cost--effectiveness of potential disease control and prevention strategies;***- Develop model-based health economics analysis tools for more accurate cost and effects analysis of vaccination programs.***- Develop an effective approach to detect, evaluate, and resolve the important issue of non-identifiability in the parameter estimation and model fitting from disease data.***- Develop user-friendly computer software packages that automate the model-based assessment toolbox for public health end-users.******The research will advance and enrich the theory of large--scale and complex dynamical systems by integrating stability and bifurcation analysis with the modern graph theory, and have direct impact on the analysis of complex and large--scale systems from science and engineering. Through interdisciplinary collaborations with infectious disease specialist, epidemiologists, public heath researchers, and public health agencies in Canada and other countries, the researcher will further develop and apply mathematical modelling as an effective assessment and investigative tool to address important public health issues related to infectious diseases. Research results are expected to inform public health policies and bring health benefits to the general public.**