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Michael Y Li Person1 #685387 Professor of Mathematics in the Department of Mathematical and Statistical Sciences at the University of Alberta, and Director of the Information Research Lab (IRL). | Mathematical Investigation of Differential Equations and Dynamical Systems - Existence, non-existence, and stability of certain type of solutions, such as periodic solutions, quasi-periodic solutions, and almost periodic solutions. Our main approach is to study the evolution of various dimensional volumes under the nonlinear flow of the differential equation. This amounts to studying the dichotomies and other asymptotic behaviours of the solutions to associated compound differential equations of various orders.
- Since 2006, due to my interests in epidemiological models in heterogeneous populations, I begin to study large-scale inter-connected systems of differential equations on networks. A network is represented by a weighted directed graph. At each vertex, a small system of differential equations is assigned, edges of the graph provide inter-connections among the vertex systems, and the strength of inter-connections can be described by the weights on edges. Large-scale systems on networks provide a mathematical framework to study many large scale from all fields of science and engineering.
The first problem of interest is the existence, uniqueness and global stability of a positive steady state. In a result of my students and myself in 2010, we have discovered a graph-theoretic approach that allows systematic construction of global Lyapunov functions for a very general class of large-scale systems on networks. Among many new problems we have solved using this approach is the open problem of the uniqueness and global stability of the endemic equilibrium in multi-group epidemic models. The graph-theoretic approach has been successfully applied by researchers to problems in many different fields of science and engineering. Other problems of interest to us are synchronization problems in coupled oscillators, ranking problems for vertices on networks, and complexity problems in large-scale systems of coupled simple equations. Some new problems we are studying includes patterns in the distributions of quantities of interest among vertices at the the equilibrium, as well as factors that impact the patterns. Improved understanding of these problems will have important applications in science and engineering problems. Mathematical Modelling of Viral Dynamics and Immune ResponsesHuman immune system is a very complex and dynamic that involves many different types of cells and immunological pathways. The immune response to infections also comes in different stages. Mathematical modeling using differential equations and dynamical systems has been used in the studies of immune response to infections of viruses, most notably the HIV. - My research interest in this area includes the modeling of the in vivo infection process of certain retro-viruses and how the immune system responds to the infection, as well the interaction of the infection, immune system and various treatment measures. One of my current projects studies the infection of HTLV-I (Human T-cell Lymphotropic Virus Type I), which is a retro virus and also an oncogenic virus. In another project, we study the HIV-1 infection in brain. The brain is a natural reservoir for the HIV-1 virus where the virus can hide in latent form in long-lived brain macrophages. One of the topics of our brain HIV-1 study is to using modeling to evaluate the effectiveness of the "shock and kill" strategy for the HIV-1 clearance.
- My research group is also conducting interdisciplinary research projects with virologists at the Li Ka-Shing Institute of Virology. In one of the recent projects, we are working with virologists, nephrologists and surgeons to investigate mechanisms and outcomes of infection from BKV and EBV among kidney transplant patients, using mathematical modeling. We expect that our results will lead to improved prognosis for transplant patients. We are also applying mathematical modeling tools to study the differences of immune responses between elite controllers of HIV-1, who can keep the HIV-1 viral load under control without having to taking anti-retroviral drug therapies, and regular HIV-1 patients. Understanding from this work will help the development of effective HIV-1 vaccines.
Mathematical Modeling of Real-Life Public Health Problems My group has several on-going interdisciplinary research projects that use mathematical models to investigate transmission dynamics and related public-health issues for specific infectious diseases. - In one project, we are working with physicians, epidemiologists and public health researchers to model the transmission dynamics of Tuberculosis (TB) in aboriginal communities in Alberta. An objective of the modeling project is to quantitatively relate various social determinants for TB to TB incidences in a community or communities. Such research will enable health-economic analysis on potential TB intervention measures that are directed at social determinants, and provide research evidence to inform policies for TB control among aboriginal populations.
- In anther project, we are developing a new methodology for estimation of HIV incidence using public health surveillance data and HIV transmission models. We are currently working with datasets from Alberta Health and China CDC. Our approach integrates the theories of dynamical systems and statistical inference. We are also developing new and effective methods for detecting and diagnosing nonidentifiability issues in parameter estimation for differential equations models.
- During the COVID-19 epidemic, our group has been collaborating with Alberta Health in providing modeling support to inform evidence-based public health responses to the pandemic.
- These real-life modeling projects inevitably involve real disease data, and calibration of models by fitting the model outcomes to data in order to determine the right range for model parameters. This requires a different skill set from that for theoretical modeling studies. Parameter estimation using Bayesian inference and maximum likelihood methods and methods for model selection are standard tools. Efficiency in numerical simulations using software packages (Matlab, R, Python, etc) is crucial for real-life modeling studies.
- Real-life modeling is not all about data, parameter estimation, and model simulations. In fact, real-life modeling presents some of the most challenging mathematical problems. One of the difficult mathematical challenges is the "nonidentifiability" issue in parameter estimation from data: infinitely many parameter values can produce the same good-fit between model outcome and data, but they lead to drastically different predictions on important quantities that are not observed in the data. How to detect the existence of nonidentifiability and determine the degree of nonidentifiability, especially in large-scale and complex models, and how to effectively reduce or remove the nonidentifiability continue to challenge mathematical modelers.
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CitationsAdd new citationList by: CiterankMap Link[2] The Impact of Quarantine and Medical Resources on the Control of COVID-19 in Wuhan based on a Household Model
Author: Shanshan Feng, Juping Zhang, Juan Li, Xiao-Feng Luo, Huaiping Zhu, Michael Y. Li, Zhen Jin Publication date: 26 February 2022 Publication info: Bulletin of Mathematical Biology, 84(4), 47 Cited by: David Price 0:03 AM 23 November 2023 GMT Citerank: (4) 679797Huaiping ZhuProfessor of mathematics at the Department of Mathematics and Statistics at York University, a York Research Chair (YRC Tier I) in Applied Mathematics, the Director of the Laboratory of Mathematical Parallel Systems at the York University (LAMPS), the Director of the Canadian Centre for Diseases Modelling (CCDM) and the Director of the One Health Modelling Network for Emerging Infections (OMNI-RÉUNIS). 10019D3ABAB, 701037MfPH – Publications144B5ACA0, 704045Covid-19859FDEF6, 715328Nonpharmaceutical Interventions (NPIs)859FDEF6 URL: DOI: https://doi.org/10.1007/s11538-021-00989-y
| Excerpt / Summary [Bulletin of Mathematical Biology, 26 February 2022]
In order to understand how Wuhan curbed the COVID-19 outbreak in 2020, we build a network transmission model of 123 dimensions incorporating the impact of quarantine and medical resources as well as household transmission. Using our new model, the final infection size of Wuhan is predicted to be 50,662 (95%CI: 46,234, 55,493), and the epidemic would last until April 25 (95%CI: April 23, April 29), which are consistent with the actual situation. It is shown that quarantining close contacts greatly reduces the final size and shorten the epidemic duration. The opening of Fangcang shelter hospitals reduces the final size by about 17,000. Had the number of hospital beds been sufficient when the lockdown started, the number of deaths would have been reduced by at least 54.26%. We also investigate the distribution of infectious individuals in unquarantined households of different sizes. The high-risk households are those with size from two to four before the peak time, while the households with only one member have the highest risk after the peak time. Our findings provide a reference for the prevention, mitigation and control of COVID-19 in other cities of the world. |
Link[3] Modeling the second outbreak of COVID-19 with isolation and contact tracing
Author: Haitao Song, Fang Liu, Feng Li, Xiaochun Cao, Hao Wang, Zhongwei Jia, Huaiping Zhu, Michael Y. Li, Wei Lin, Hong Yang, Jianghong Hu, Zhen Jin Publication date: 1 October 2022 Publication info: Discrete & Continuous Dynamical Systems - B, 2022, Volume 27, Issue 10: 5757-5777. Cited by: David Price 12:24 PM 1 December 2023 GMT Citerank: (5) 679791Hao WangProfessor in the Department of Mathematical and Statistical Sciences at the University of Alberta.10019D3ABAB, 679797Huaiping ZhuProfessor of mathematics at the Department of Mathematics and Statistics at York University, a York Research Chair (YRC Tier I) in Applied Mathematics, the Director of the Laboratory of Mathematical Parallel Systems at the York University (LAMPS), the Director of the Canadian Centre for Diseases Modelling (CCDM) and the Director of the One Health Modelling Network for Emerging Infections (OMNI-RÉUNIS). 10019D3ABAB, 701037MfPH – Publications144B5ACA0, 704045Covid-19859FDEF6, 715294Contact tracing859FDEF6 URL: DOI: https://doi.org/10.3934/dcdsb.2021294
| Excerpt / Summary [Discrete & Continuous Dynamical Systems - B, October 2022]
The first case of Corona Virus Disease 2019 (COVID-19) was reported in Wuhan, China in December 2019. Since then, COVID-19 has quickly spread out to all provinces in China and over 150 countries or territories in the world. With the first level response to public health emergencies (FLRPHE) launched over the country, the outbreak of COVID-19 in China is achieving under control in China. We develop a mathematical model based on the epidemiology of COVID-19, incorporating the isolation of healthy people, confirmed cases and contact tracing measures. We calculate the basic reproduction numbers 2.5 in China (excluding Hubei province) and 2.9 in Hubei province with the initial time on January 30 which shows the severe infectivity of COVID-19, and verify that the current isolation method effectively contains the transmission of COVID-19. Under the isolation of healthy people, confirmed cases and contact tracing measures, we find a noteworthy phenomenon that is the second epidemic of COVID-19 and estimate the peak time and value and the cumulative number of cases. Simulations show that the contact tracing measures can efficiently contain the transmission of the second epidemic of COVID-19. With the isolation of all susceptible people or all infectious people or both, there is no second epidemic of COVID-19. Furthermore, resumption of work and study can increase the transmission risk of the second epidemic of COVID-19. |
Link[4] Canada’s provincial COVID-19 pandemic modelling efforts: A review of mathematical models and their impacts on the responses
Author: Yiqing Xia, Jorge Luis Flores Anato, Caroline Colijn, Naveed Janjua, Mike Irvine, Tyler Williamson, Marie B. Varughese, Michael Li, Nathaniel Osgood, David J. D. Earn, Beate Sander, Lauren E. Cipriano, Kumar Murty, Fanyu Xiu, Arnaud Godin, David Buckeridge, Amy Hurford, Sharmistha Mishra, Mathieu Maheu-Giroux Publication date: 25 July 2024 Publication info: Canadian Journal of Public Health, Volume 115, pages 541–557, (2024) Cited by: David Price 0:36 AM 10 December 2024 GMT
Citerank: (14) 679712CANMOD – PeopleCANMOD is a national network, with members located across the country and associated with a broader Emerging Infectious Disease Modelling (EIDM) initiative. We are a community of modellers, statisticians, epidemiologists, public health decision-makers, and those implementing and delivering interventions.10019D3ABAB, 679752Amy HurfordAmy Hurford is an Associate Professor jointly appointed in the Department of Biology and the Department of Mathematics and Statistics at Memorial University of Newfoundland and Labrador. 10019D3ABAB, 679757Beate SanderCanada Research Chair in Economics of Infectious Diseases and Director, Health Modeling & Health Economics and Population Health Economics Research at THETA (Toronto Health Economics and Technology Assessment Collaborative).10019D3ABAB, 679761Caroline ColijnDr. Caroline Colijn works at the interface of mathematics, evolution, infection and public health, and leads the MAGPIE research group. She joined SFU's Mathematics Department in 2018 as a Canada 150 Research Chair in Mathematics for Infection, Evolution and Public Health. She has broad interests in applications of mathematics to questions in evolution and public health, and was a founding member of Imperial College London's Centre for the Mathematics of Precision Healthcare.10019D3ABAB, 679775David BuckeridgeDavid is a Professor in the School of Population and Global Health at McGill University, where he directs the Surveillance Lab, an interdisciplinary group that develops, implements, and evaluates novel computational methods for population health surveillance. He is also the Chief Digital Health Officer at the McGill University Health Center where he directs strategy on digital transformation and analytics and he is an Associate Member with the Montreal Institute for Learning Algorithms (Mila).10019D3ABAB, 679776David EarnProfessor of Mathematics and Faculty of Science Research Chair in Mathematical Epidemiology at McMaster University.10019D3ABAB, 679844Mathieu Maheu-GirouxCanada Research Chair (Tier 2) in Population Health Modeling and Associate Professor, McGill University.10019D3ABAB, 679855Nathaniel OsgoodNathaniel D. Osgood is a Professor in the Department of Computer Science and Associate Faculty in the Department of Community Health & Epidemiology at the University of Saskatchewan.10019D3ABAB, 679856Naveed Zafar JanjuaDr. Naveed Zafar Janjua is an epidemiologist and senior scientist at the BC Centre for Disease Control and Clinical Associate Professor at School of Population and Public Health, University of British Columbia. Dr. Janjua is a Medical Doctor (MBBS) with a Masters of Science (MSc) degree in Epidemiology & Biostatistics and Doctorate in Public Health (DrPH). 10019D3ABAB, 679880Sharmistha MishraSharmistha Mishra is an infectious disease physician and mathematical modeler and holds a Tier 2 Canadian Research Chair in Mathematical Modeling and Program Science.10019D3ABAB, 679893Kumar MurtyProfessor Kumar Murty is in the Department of Mathematics at the University of Toronto. His research fields are Analytic Number Theory, Algebraic Number Theory, Arithmetic Algebraic Geometry and Information Security. He is the founder of the GANITA lab, co-founder of Prata Technologies and PerfectCloud. His interest in mathematics ranges from the pure study of the subject to its applications in data and information security.10019D3ABAB, 701020CANMOD – PublicationsPublications by CANMOD Members144B5ACA0, 701037MfPH – Publications144B5ACA0, 704045Covid-19859FDEF6 URL: DOI: https://doi.org/10.17269/s41997-024-00910-9
| Excerpt / Summary [Canadian Journal of Public Health, 25 July 2024]
Setting: Mathematical modelling played an important role in the public health response to COVID-19 in Canada. Variability in epidemic trajectories, modelling approaches, and data infrastructure across provinces provides a unique opportunity to understand the factors that shaped modelling strategies.
Intervention: Provinces implemented stringent pandemic interventions to mitigate SARS-CoV-2 transmission, considering evidence from epidemic models. This study aimed to summarize provincial COVID-19 modelling efforts. We identified modelling teams working with provincial decision-makers, through referrals and membership in Canadian modelling networks. Information on models, data sources, and knowledge translation were abstracted using standardized instruments.
Outcomes: We obtained information from six provinces. For provinces with sustained community transmission, initial modelling efforts focused on projecting epidemic trajectories and healthcare demands, and evaluating impacts of proposed interventions. In provinces with low community transmission, models emphasized quantifying importation risks. Most of the models were compartmental and deterministic, with projection horizons of a few weeks. Models were updated regularly or replaced by new ones, adapting to changing local epidemic dynamics, pathogen characteristics, vaccines, and requests from public health. Surveillance datasets for cases, hospitalizations and deaths, and serological studies were the main data sources for model calibration. Access to data for modelling and the structure for knowledge translation differed markedly between provinces.
Implication: Provincial modelling efforts during the COVID-19 pandemic were tailored to local contexts and modulated by available resources. Strengthening Canadian modelling capacity, developing and sustaining collaborations between modellers and governments, and ensuring earlier access to linked and timely surveillance data could help improve pandemic preparedness. |
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