The road traveled by....

I entered the applied mathematics PhD program, the first Chinese PhD program with a focus on functional differential equations, in 1984. My thesis supervisor, Professor Senlin Li, is highly renowned for his pioneering work on constructing piecewise Liapunov functions for stability analysis. Professor Li gave me a thesis project to expand his early work to infinite dimensional dynamical systems. I happily followed his advice, but managed to convince him that I could write another "component" on the fundamental theory of neutral functional differential equations with infinite delay. This second component was where my heart and eventually my energy went to, so I virtually wrote two theses. I am forever indebted to Professor Li for allowing me to choose this second "component". For this reason, I always advice my students that they should figure out where their interest goes when picking up their research topics.

I nevertheless spent much of my PHD time for an extracurricular activity in a "profitable" applied mathematics project. My roommate (a future chemist) linked me to a group of epidemiologists at the Institute of Parasitic Infections, and I became fascinated about the potential use of differential equations to evaluate the role of agricultural activities in sustaining the schistosomiasis endemic in the province. We developed a novel differential equations model that caught the attention of a WHO delegation- this was my first interdisciplinary collaboration and I was richly awarded. The Institute sent me a research contract (8000 yuans, a huge amount at that time). My university decided that I could not take a single penny from the contract since I was only a student, so the Institute decided to give me and my teammates a self-guided tour of the newly discovered Zhangjiajie National Park—touted as the Grand Canyon of China that became instantly famous after Avatar was filmed there.

I continued this scenery journey "the interface of the dynamical systems and biological sciences", through multiple stopovers (University of Szeged, University of Memphis, University of Alberta, in that order) until I became a faculty member at York University in 1990, where I established the Laboratory for Industrial and Applied Mathematics (LIAM), and am currently serving as the inaugural director of the York Emergency Mitigation, Engagement, Response, and Governance Institute (Y-EMERGE). The first stop after my PhD study was Bolyai Institute. The one-month visit marked the beginning of a rewarding collaboration with three generations of Szeged scientists represented by László Hatvani, Tibor Krisztin and Gergely Röst. The university bestowed me with Doctor Honoris Causa in 2016.

The collaboration with Tibor was quickly expanded to a team effort with József Terjéki (Szeged) and John Haddock (University of Memphis), and we produced an invariance principle of Lyapunov-Razumikhin type for neutral functional differential equations (remember the other "component" of my PhD thesis?). The Krisztin-Wu collaboration was then intensified, when both of us were awarded Humboldt fellowships hosted at University of Giessen. It was there I learnt the geometric theory of dynamical systems from Tibor and our host, Professor Hans-otto Walther. The fellowship in Giessen (1996-97) produced the 243-page paper that developed a systematic geometric theory to give a complete description of the geometric and topological structures of the global attractor, the Krisztin-Walther-Wu spindle, for a delayed feedback system. My journey in fundamental research is so joyful because of these good companies.

Before joining York, I had a sojourn stay at University of Alberta as an inaugural G. Kaplan postdoctoral fellow. Edmonton, or the Edmonton School of Differential Equations (as Jean Mawhin called) was a warm place for me even when it was at -40C. Here I learnt algebraic topology and topological methods in nonlinear analysis from Lyne Erbe and Wieslaw Krawcewicz, and we developed the S^1-degree theoretic framework for the global bifurcation analysis. During this period, my extracurricular activity in mathematical biology became part of my professional life thanks to Professor Herb Freedman, who taught me the arts and sciences of bidirectionally translating between biological processes and differential equations! My work with Herb sets a strong foundation for my future "recreational" exercise in disease modelling.

This exercise started from a call by Arvind Gupta, the day after the 2003-04 SARS was imported to Canada. Arvind called me on behalf of the Network of Centers of Excellence (NCE Mitacs/Mprime), to explore my interest in establishing a national SARS-modeling team to provide real-time support for managing the outbreak. He gave me 24 hours to consider, but I accepted the challenge only a few hours later after securing support from fellow modellers (Fred Brauer, Paulien van den Driessche, for example), and domain experts from both provincial and federal health agencies. My acceptance was however conditional on 1). having unspecified funding support (no time to write a proposal); and 2). commitment for continuing support after the outbreak. Arvind accepted the 1st condition and allowed us to submit any expense for reimbursement. It proved that Arvind is a real master in managing public funding as we were so busy in the modeling work that we did not have time spending! At the end of the SARS outbreak, I rushed to a conclusion that it is the good ideas and networking, not funding support, that paves the road to success in interdisciplinary collaboration.

I, however, quickly realized that funding support for large-scale collaborations in applied mathematics is important. Mprime did fund the SARS modeling team (after we submitted a proposal!), and this support turned to be critical for trainee engagement. Started from the 2004 MSRI-PIMS-MITACS thematic program held in the beautiful Banff International Research Station (BIRS), we initiated a Summer School series "Mathematics for Public Health". This became an important component of the capacity building as it teaches a common language and platform within which different groups can communicate and collaborate effectively for transferring modelling technologies into policy recommendations. The summer school series has produced many students working now as modellers and health economists in universities, governmental agencies, and industrial organizations, creating a group of scientists working with different stakeholders to develop a reciprocal linkage between modelling and applications.

The SARS project continued for a decade (2004-14) to support us work closely with the Public Health Agency of Canada to coordinate the re-alignment of research and collaboration of key Canadian modelers during 2009 pandemic influenza. In parallel, another NCE center, GEOIDE, funded a project on geo-simulation of disease spreading. Co-led with the GIS expert Dongmei Chen and the computer scientist Bernard Moulin, the team developed novel geo-simulation tools to inform spatial-temporal hotspots of emerging infectious diseases including Lyme disease, West Nile virus and avian influenza. Subsequently, with the infection control expert Andrew Morris and funded by the Collaborative Health Research program, "the best team that one can have in Canada" was assembled to develop an Antimicrobial Resistance Diversity Index to guide initiatives and investment in public health, antimicrobial stewardship and infection Control. These projects have built the reciprocal linkages enabling rapid response. So in February 2020, upon requests from the Fields Institute, we were able to establish the National COVID-19 Modeling Rapid Response Task Force to coordinate an interdisciplinary effort of using mathematical modeling to inform COVID-19 pandemic decision making. The task force was created way before the WHO’s declaration of Covid-19 global pandemic, but funding to the task force came later (remember our SARS modeling team experience?) thanks to the leadership of Kumar Murty.

I must mention the collaboration with Sanofi, a vaccine producer, to describe the on-going journey through the academic-public-industrial triangle. The collaboration is motivated by our joint belief that mathematical modeling (more precisely, dynamic modeling) must be the foundation of health economics analysis required in pharmaceutical product submission to regulatory agencies for approval. The York-Sanofi collaboration, funded initially by the Industrial Research Chair program, grew and elevated organically form project-based collaborations to program- and capacity building-oriented institutional partnership to allow the maximal flexibility in addressing the intrinsic challenge of industrial collaboration imposed to a modeller in the academic environment: short timeline for delivery, constant change of research/development focus, and rapid promotion of collaborating scientists in the industry.

Over the past two decades, I have seen a paradigm shift towards increasingly recognizing the roles of mathematical modelling in decision making inside government and industrial organizations. This paradigm shift provides an unprecedent opportunity for the next generation of applied mathematicians to choose their career paths in different sectors.

I have benefited so much from my training in dynamical systems and differential equations. These not only are among major instruments in my toolkits used to solve industrial and applied problems, but more importantly provide me scientific lens to observe, interpret and formulate the applied problems. It was the most significant moment in my scientific journey when I realized how the dynamic bifurcation theory had guided me in my design of the models and their analyses, both theoretically and numerically, to provide the scenario analyses for the end-users.