- http://www.ualberta.ca/~myli
Michael Y Li
University of Alberta, Mathematical and Statistical Sciences, Faculty Member
- Global dynamics of coupled systems on complex networks, Modeling the transmission dynamics of infectious diseases, Modeling immune response to viral infections, Public health research, Applied Mathematics, Mathematical Modeling, and 20 moreMathematical Epidemiology, Immune response, Lyapunov functions, Global stability, HTLV (Retroviruses), Mathematical Modelling, Infectious Diseases, Infectious disease epidemiology, Epidemic Modeling, Transmission dynamics of infectious diseases, Basic Reproduction Number, Li-Muldowney, Compound Matrix, SEIR Model, Compound matrices, Compound matrix method, Li-Muldowney Method, Li and Muldowney, Endemic Equilibrium, and Threshold Theoremedit
- Dr. Michael Y. Li is a Professor of Mathematics at the University of Alberta. His research interests include complex ... moreDr. Michael Y. Li is a Professor of Mathematics at the University of Alberta. His research interests include complex dynamical systems, nonlinear differential equations, mathematical modeling of the transmission dynamics of infectious diseases, viral dynamics and immune responses, and integration of mathematical modeling, statistical methodology and machine learning for data analysis and solve complex problems.edit
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Various eeects of disease caused death on the host population is studied in an epidemic model of SIR type. The exponential rate for natural birth and death is assumed to be equal so that the total population is balanced in the absence of... more
Various eeects of disease caused death on the host population is studied in an epidemic model of SIR type. The exponential rate for natural birth and death is assumed to be equal so that the total population is balanced in the absence of the disease. The model has the surprising feature that it requires a simple mathematical analysis while revealing interesting and robust epidemiological phenomena, some of which would not be easily observed in more complicated models.
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ABSTRACT. In this paper, we treat two examples to illustrate the idea of optimal control in two types of disease models. In the first example, we consider an epidemic model with two different incidence forms. A percentage of the... more
ABSTRACT. In this paper, we treat two examples to illustrate the idea of optimal control in two types of disease models. In the first example, we consider an epidemic model with two different incidence forms. A percentage of the population are vaccinated in the model to ...
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Research Interests: Mathematics, Health Sciences, Biology, Virology, Medicine, and 15 moreBiological Sciences, Humans, Mathematical Sciences, Virus, Mathematical Analysis, Microbiology and Immunology, Mathematical Model, Adult, Global stability, Virus Dynamics, Basic Reproduction Number, Cell Proliferation, Mathematical Biosciences, Endemic Equilibrium, and logistic growth
Research Interests: Mathematics, Applied Mathematics, Epidemiology, Pure Mathematics, Mathematical Analysis, and 13 moreStability Theory, Graph, Global stability, Lyapunov functions, Mathematical Analysis and Applications, Basic Reproduction Number, Lyapunov function, Distributed delay, Epidemic models, Epidemic Model, Electrical And Electronic Engineering, Endemic Equilibrium, and Time Delays
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Research Interests: Applied Mathematics, Dynamical Systems, Biology, Mathematical Modeling, Mathematical Modelling, and 15 moreMedicine, Biological Sciences, Population, Humans, Mathematical Sciences, Hiv Infection, Dynamic systems, Epidemic Modeling, Clearance, Mathematical Model, Hiv Aids, Adult, Basic Reproduction Number, Dynamic Systems, and Mathematical Biosciences
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The intestine plays an important role in nutrient digestion and absorption, microbe defense, and hormone secretion. Although major cell types have been identified in the mouse intestinal epithelium, cell type–specific markers and... more
The intestine plays an important role in nutrient digestion and absorption, microbe defense, and hormone secretion. Although major cell types have been identified in the mouse intestinal epithelium, cell type–specific markers and functional assignments are largely unavailable for human intestine. Here, our single-cell RNA-seq analyses of 14,537 epithelial cells from human ileum, colon, and rectum reveal different nutrient absorption preferences in the small and large intestine, suggest the existence of Paneth-like cells in the large intestine, and identify potential new marker genes for human transient-amplifying cells and goblet cells. We have validated some of these insights by quantitative PCR, immunofluorescence, and functional analyses. Furthermore, we show both common and differential features of the cellular landscapes between the human and mouse ilea. Therefore, our data provide the basis for detailed characterization of human intestine cell constitution and functions, which...
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The state of an infectious disease can represent the degree of infectivity of infected individuals, or susceptibility of susceptible individuals, or immunity of recovered individuals, or a combination of these measures. When the disease... more
The state of an infectious disease can represent the degree of infectivity of infected individuals, or susceptibility of susceptible individuals, or immunity of recovered individuals, or a combination of these measures. When the disease progression is long such as for HIV, individuals often experience switches among different states. We derive an epidemic model in which infected individuals have a discrete set of states of infectivity and can switch among different states. The model also incorporates a general incidence form in which new infections are distributed among different disease states. We discuss the importance of the transmission–transfer network for infectious diseases. Under the assumption that the transmission–transfer network is strongly connected, we establish that the basic reproduction number R0 is a sharp threshold parameter: if R0≤1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out; if R0>1, the disease-free equilibrium is unstable, the system is uniformly persistent and initial outbreaks lead to persistent disease infection. For a restricted class of incidence functions, we prove that there is a unique endemic equilibrium and it is globally asymptotically stable when R0>1. Furthermore, we discuss the impact of different state structures on R0, on the distribution of the disease states at the unique endemic equilibrium, and on disease control and preventions. Implications to the COVID-19 pandemic are also discussed.
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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... more
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...
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Research Interests: Mathematics, Applied Mathematics, Pure Mathematics, Neural Network, Bifurcation, and 10 moreMathematical Analysis and Applications, Global existence, Bifurcation Analysis, Electrical And Electronic Engineering, Ordinary Differential Equation, Neural Network Model, Hopf Bifurcation, Normal Form, Periodic Solution, and Neutral Differential Equation
A disease is infectious if the causative agent, whether a virus, bacterium, protozoa, or toxin, can be passed from one host to another through modes of transmission such as direct physical contact, airborne droplets, water or food,... more
A disease is infectious if the causative agent, whether a virus, bacterium, protozoa, or toxin, can be passed from one host to another through modes of transmission such as direct physical contact, airborne droplets, water or food, disease vectors, or mother to newborn.
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The ongoing outbreak of the novel coronavirus pneumonia (also known as COVID-19) has triggered a series of stringent control measures in China, such as city closure, traffic restrictions, contact tracing and household quarantine. These... more
The ongoing outbreak of the novel coronavirus pneumonia (also known as COVID-19) has triggered a series of stringent control measures in China, such as city closure, traffic restrictions, contact tracing and household quarantine. These containment efforts often lead to changes in the contact pattern among individuals of the population. Many existing compartmental epidemic models fail to account for the effects of contact structure. In this paper, we devised a pairwise epidemic model to analyze the COVID-19 outbreak in China based on confirmed cases reported during the period February 3rd--17th, 2020. By explicitly incorporating the effects of family clusters and contact tracing followed by household quarantine and isolation, our model provides a good fit to the trajectory of COVID-19 infections and is useful to predict the epidemic trend. We obtained the average of the reproduction number $R=1.494$ ($95\%$ CI: $1.483-1.507$) for Hubei province and $R=1.178$ ($95\%$ CI: $1.145-1.158$...
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In this chapter, we present some standard mathematical methods for the analysis of compartmental epidemic models. We have chosen five classic epidemic models to demonstrate these methods. We start from the basic Kermack–McKendrick model... more
In this chapter, we present some standard mathematical methods for the analysis of compartmental epidemic models. We have chosen five classic epidemic models to demonstrate these methods. We start from the basic Kermack–McKendrick model and progressively expand it to a model with demography, and then introduce the Ross–MacDonald model for malaria. Each model is chosen to illustrate a specific mathematical approach for model analysis: the method of first integrals and level curves, the phase-line analysis, phase-plane analysis, reduction of dimension using homogeneity, and monotone dynamical systems. The general mathematical theories applied in this chapter are provided in Chapter 3 for reference and in-depth learning. Students in mathematics have a chance to learn these general theories in the setting of epidemic models and see how abstract theories of differential equations are applied to real-world problems. Students in public health and biological sciences will be able to learn the basic model analysis and gain exposure to some abstract mathematical concepts such as stability and bifurcations explained in the context of epidemiology, as well as to the theory of modern differential equations.
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Research Interests: Chemical Engineering, Applied Mathematics, Biomedical Engineering, Biology, Communicable Diseases, and 13 moreMathematical Modeling, Stability, Medicine, Disease Outbreaks, Humans, Computer Simulation, Transmission dynamics of infectious diseases, Bifurcation, Disease Carriers, Lyapunov functions, Basic Reproduction Number, Music Information Dynamics, and Carrier state
Research Interests: Immune response, Mathematical Biology, Biological Sciences, Humans, Mathematical Sciences, and 15 moreCytotoxic T lymphocytes, Global Attractor, Oscillations, Mathematical Model, Modeling immune response to viral infections, Viral Infection, Currency fluctuations and impact on export and import, CTL, Biological clocks, Basin of Attraction, Multiple equilibria, Hopf Bifurcation, Chronic Infection, attractor, and Periodic Solution
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Research Interests: Immunology, Mathematical Biology, Biology, Medicine, Biological Sciences, and 15 moreHumans, Mathematical Sciences, Mathematical Analysis, CD, Mathematical Model, Peripheral blood lymphocyte, Lyapunov functions, CTL, Basic Reproduction Number, Lyapunov function, Global Dynamics, CTL Response, Cytotoxic T cells, Carrier state, and Peripheral blood
Research Interests: Mathematics, Immunology, Immune response, Biology, Mathematical Modeling, and 15 moreMathematical Modelling, Medicine, Gene expression, Retroviruses, Biological Sciences, Humans, Mathematical Sciences, Inflammatory disease, Immune system, Mathematical Concepts, Adult, Global stability, Retrovirus, Chronic Infection, and Compartmental Model
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In recent studies, global Hopf branches were investigated for delayed model of HTLV-I infection with delay-independent parameters. It is shown in [8, 9] that when stability switches occur, global Hopf branches tend to be bounded, and... more
In recent studies, global Hopf branches were investigated for delayed model of HTLV-I infection with delay-independent parameters. It is shown in [8, 9] that when stability switches occur, global Hopf branches tend to be bounded, and different branches can overlap to produce coexistence of stable periodic solutions. In this paper, we investigate global Hopf branches for delayed systems with delay-dependent parameters. Using a delayed predatorprey model as an example, we demonstrate that stability switches caused by varying the time delay are accompanied by bounded global Hopf branches. When multiple Hopf branches exist, they are nested and the overlap produces coexistence of two or possibly more stable limit cycles.
The dynamics of the transmission and spread of infectious diseases are known to be highly complex largely due to the heterogeneity of the host population and the ecology of the pathogens that causes the disease. Factors contributing to... more
The dynamics of the transmission and spread of infectious diseases are known to be highly complex largely due to the heterogeneity of the host population and the ecology of the pathogens that causes the disease. Factors contributing to the heterogeneity of the host population include age distributions, social and ethnical groups, and spatial distributions, all of which can create complex contact patterns among hosts. Ecological factors for disease pathogens include life cycles, disease vectors, multiple hosts, and environmental influences due to local seasonal changes and large-scale climate changes. Mathematical models that incorporate these factors of heterogeneity often result in a large-scale system of nonlinear differential or difference equations that has a high dimension, multi-components and multi-parameters. While these type of models are more realistic than the classical SIR or SEIR models, its mathematical analysis is highly nontrivial because of the high-dimensionality a...
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Research Interests: Mathematics, Applied Mathematics, Graph Theory, Mathematical Epidemiology, Dynamics on Networks, and 10 moreMathematical Modelling, Pure Mathematics, Epidemic Modeling, Mathematical Modeling of Infectious Diseases, Heterogeneous Distributed Systems, Global stability, Lyapunov functions, Lyapunov function, Epidemic Model, and Endemic Equilibrium
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Research Interests: Chemical Engineering, Applied Mathematics, Biomedical Engineering, Biology, Medicine, and 10 moreMarkov-chain model, Infectious Disease, Density dependence, Hiv Infection, Mathematical Model, Immune system, Basic Reproduction Number, Disease Progression, Mathematical Biosciences, and Endemic Equilibrium
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Research Interests: Global Health, Communicable Diseases, Biological Sciences, Antiretroviral Therapy, Humans, and 10 moreMathematical Sciences, Infectious Disease, Mathematical Model, Global stability, Highly Active Antiretroviral Therapy, Basic Reproduction Number, Lyapunov function, Disease Progression, Endemic Equilibrium, and Medical and Health Sciences
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Research Interests: Mathematical Biology, Virology, Mathematical Modelling, Hepatitis C, Virus-Host Interactions, and 11 moreBiological Sciences, Hepatitis B, Humans, Mathematical Sciences, Oscillations, Virus Dynamics, Basic Reproduction Number, Lyapunov function, Intracellular delay, Host Pathogen Interactions, and HIV infections
Research Interests: Immune response, Biology, Medicine, Biological Sciences, Humans, and 12 moreComputer Simulation, Mathematical Sciences, Time Delay, Oscillations, Mathematical Model, Viral Infection, Basic Reproduction Number, Frequency Response Function, Biological clocks, Basin of Attraction, Hopf Bifurcation, and Periodic Solution
This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies. The book includes mathematical descriptions of epidemiological... more
This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies. The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis. Matlab codes are also included for numerical implementations.
It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases. Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.
It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases. Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.