Michael Li's Publications

Selected Publications, Dr. Michael Y. Li, University of Alberta

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Research Interests:

1. Modeling Research in Public Health

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Why is it difficult to accurately predict the COVID-19 epidemic? (with W. Roda, M. Varughese, and D. Han) pdf Infectious Disease Modeling, 5, 271-281, 2020.
Global dynamics of a discrete age-structured SIR epidemic model with applications to measles vaccination strategies, (with L. Zhou, Y. Wang, and Y. Xiao) pdf Math. Biosci. 308, 27-37, 2019.
Efficacy of screening and treatment of latent tuberculosis infection, (with M. Varughese and R. Long) pdf Mathematical Population Studies 24, 21-36, 2017, doi:10.1080/08898480.2014.998546
A mathematical modeling study of the HIV epidemics at two rural townships in the Liangshan Prefecture of the Sichuan Province of China, (with Z. Su, C. Dong, P. Li, H. Deng, Y. Gong, S. Zhong, M. Wu, Y. Ruan, G. Qin, W. Yang, Y. Shao) pdf Infectious Disease Modeling, 1, 3-11, 2016, doi: http://dx.doi.org/10.1016/j.idm.2016.05.001
Preventing tuberculosis in the foreign-born population of Canada: a mathematical modelling study, (with B. Varughese, D. Langlois-Klassen and R. Long) pdf Int. J. Tuberc. Lung Dis., 18(4), 405-412, 2014

2. Viral Dynamics and Modeling of Immune Responses

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Modeling the Effects of Latency Reversing Drugs During HIV-1 and SIV Brain Infection with Implications for the "Shock and Kill" Strategy, (with W. C. Roda, S. Liu, and C. Power) Online Bull. Math. Biol., 83, 39, 2021. doi: 10.1007/s11538-021-00875-7
Viral dynamics of HIV-1 with CTL immune response, (with A. Wang) pdf DCDS-B, 26, 2257-72, 2021. doi: 10.3934/dcdsb.2020212
HIV-1 persistence in the central nervous system: viral and host determinants during antiretroviral therapy, (with E.F. Balcom, W. C. Roda, E. A. Cohen, and C. Power) pdf Curr. Opin. Virol., 38, 54-62, 2019, doi:10.1016/j.coviro.2019.06.004
Modeling brain lentiviral infections during antiretroviral therapy in AIDS, (with W. C. Roda, M. S. Akinwumi, E. L. Asahchop, B. B. Gelman, K. W. Witwer, and C. Power) pdf J. Neurovirol., 2017, doi:10.1007/s13365-017-0530-3
Backward bifurcation in a mathematical model for HIV infection in vivo with anti-retroviral treatment, (with L. Wang) pdf Nonl. Anal. RWA, 17, 147-160, 2014
Stable and transient periodic oscillations in a mathematical model for CTL response to HTLV-I infection, (with J. Lang) pdf J. Math. Bio. 65, 181-199, 2012
Joint effects of mitosis and intracellular delay on viral dynamics: two-parameter bifurcation analysis, (with H. Shu) pdf J. Math. Bio. 64, 1005-1020, 2012
Global dynamics of a mathematical model for HTLV-I infection of CD4+ T cells with delayed CTL response, (with H. Shu) pdf Nonlinear Anal. Real World Appl. 13, 1080-1092, 2012.
Multiple stable periodic oscillations in a mathematical model of CTL response to HTLV-I infection, (with H. Shu) pdf J. Math. Biol. 73, 1774-1793, 2011.
Modelling the role of Tax expression in HTLV-I persistence in vivo, (with A. Lim) pdf Bull. Math. Bio. 73, 3008-3029, 2011.
Impact of intracellular delays and target-cell dynamics on in vivo viral infections, (with H. Shu) pdf SIAM J. Appl. Math. 70, 2434-2448, 2010.
Multi-stability in a model for CTL response to HTLV-I infection and its implications to HAM/TSP development and prevention, (with H. Gomez-Acevedo and S. Jacobson) pdf Bull. Math. Bio. 72, 681-696, 2010.
Global dynamics of an in-host viral model with intracellular delays, (with H. Shu) pdf Bull. Math. Bio. 72, 1429-1505, 2010.
Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells. (with L. Wang) pdf Math. Biosci. 200, 44-57, 2006.
Backward bifurcation in a model for HTLV-I infection of CD4+ T cells. (with H. Gomez-Acevedo) pdf Bull. Math. Bio. 67, 101-114, 2005.
Mathematical Analysis of the global dynamics of a model for HTLV-I infection of T cells. (with H. Gomez-Acevedo) pdf Canadian Appl. Math. Quart.10, 71-86, 2002.
Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression. (with D. Kirschner and L. Wang) pdf Math. Biosci. 179, 207-217, 2002.

3. Population Dynamics of Infectious Diseases

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Epidemic models with discrete state structures, (with S. Liu) pdf Physica D 422 5262-5296, 2021. doi:10.1016/j.physd.2021.132903
Global dynamics of an infinite dimensional epidemic model with nonlocal state structures, (with Z. Qiu and Z. Shen) pdf J. Differential Equations 265 5262-5296, 2018.
Turning points and relaxation oscillation cycles in simple epidemic models, (with W. Liu, C. Shan, and Y. Yi) pdf SIAM J. Appl. Math., 76, 663-687, 2016
Impacts of migration and immigration on disease transmission dynamics in heterogeneous populations, (with H. Guo) pdf DCDS-B 17, 2413-2430, 2012
Global dynamics of a general class of multistage models for infectious diseases, (with H. Guo and Z. Shuai) pdf SIAM J. Appl. Math. 72, 261-279, 2012
Global dynamics of a staged-progression model for HIV/AIDS with amelioration, (with H. Guo) pdf Nonlinear Anal. RWA 12, 2529-2540, 2011.
Density dependence in disease incidence and its impacts on transmission dynamics, (with R. de Boer) pdf Canadian Applied Math. Quarterly 19, 195-218, 2011.
Modeling the effects of carriers on transmission dynamics of infectious diseases, (with D. Kalajdzievska) pdf Math. Biosci. & Eng. 8, 711-722, 2011.
Global stability of an epidemic model in a patchy environment, (with Z. Shuai) pdf Canadian Appl. Math. Quart. 17, 175-187, 2009.
Global dynamics of a staged-progression model with amelioration for infectious diseases, (with H. Guo) pdf J. Bio. Dyn. 2, 154-168, 2008.
Global dynamics of a staged progression model for infectious diseases, (with H. Guo) pdf Math. Biosci. Eng. 3, 513-525, 2006.
Global stability in a mathematical model of tuberculosis, (with H. Guo) pdf Can. Appl. Math. Q 14, 185-197, 2006.
Global stability in some SEIR models. (with L. Wang) pdf Mathematical Approaches for Emerging and Reemerging Infectious Diseases Part II: Models, Methods and Theory (Castillo-Chavez et al., eds.), IMA Volumes in Mathematics and its Applications 126, Springer-Verlag, 2002, pp. 295-311.
A study of the effects of disease caused death in a simple epidemic model.(with J. R. Graef and L. Wang) reprint Discr. Cont. Dynam. Sys., Special vol., 288-300,1997.

4. Complex Systems - Graph-Theoretic Method for Lyapunov Functions

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Impact of network connectivity on the synchronization and global dynamics of coupled systems of differential equations, (with P. Du) pdf Physica D, 287, 32-42, 2014
Global Lyapunov functions and a hierarchical control scheme for networks of robotic agents, (with J. Maidens) pdf American Control Conference (ACC), 4050-4055, 2013
Global-stability problem for coupled systems of differential equations on networks, (with Z. Shuai) pdf J. Differential Equations 248, 1-20, 2010.
Global stability of multi-group epidemic models with distributed delays, (with Z. Shuai and C. Wang) pdf J. Math. Anal. Appl. 361, 38-47, 2010.
A graph-theoretic approach to the method of global Lyapunov functions, (with H. Guo and Z. Shuai) pdf Proc. Amer. Math. Soc. 136, 2793-2802, 2008.
Global stability of the endemic equilibrium of multigroup SIR epidemic models, (with H. Guo and Z. Shuai) pdf Canadian Appl. Math. Quaert. 14, 259-284, 2006.

5. Li-Muldowney Theory and its Applications

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Global Hopf bifurcation analysis of a Nicholson's blowflies equation of neutral type, (with C. Wang and J. Wei) pdf J Dyn. Diff. Equat., 26, 165-179, 2014
Global Hopf branches and multiple limit cycles in a delayed Lotka-Volterra predator-prey model, (with X. Lin and H. Wang) pdf DCDS-B, 19, 747-760, 2014
Global Hopf bifurcation analysis of a neuron network model with time delays, (with J. Wei) pdf Infinite Dimensional Dynamical Systems, Fields Institute Communications, 64, 141-168, 2013
Bifurcation analysis in a neutral differential equation, (with Y. Qu and J. Wei) pdf J. Math. Anal. Appl. 378, 387-402, 2011.
Hopf bifurcation analysis for a delayed Nicholson Blowflies equation. (with J. Wei) pdf Nonlinear Analysis 60, 1351-1367, 2005.
Global existence of periodic solutions in a tri-neuron network model with delays. (with J. Wei) pdf Physica D 198, 106-119, 2004.
Global stability of an SEIS model with recruitment and varying total population. (with M. Fan and K. Wang) pdf Math. Biosci. 170, 199-208, 2001.
Global dynamics of an SEIR model with vertical transmission. (with H. L. Smith and L. Wang) pdf SIAM J. Appl. Math. 62, 58-69, 2001.
Global dynamics of SEIR models with vertical transmission and saturation incidence. (with L. Wang) reprint Dynam. Sys. Appl. 3, 603-610, 2001.
Dynamics of differential equations on invariant manifolds. (with J. S. Muldowney) pdf J. Differential Equations 168, 295-320, 2000.
Global stability for SEIRS models in epidemiology. (with J. S. Muldowney and P. Van den Driessche).  pdf Canadian  Appl. Math. Quart. 7, 409-425, 1999.
Global dynamics of a SEIR model with a varying total population size. (with J. R. Graef, L. Wang, and J. Karsai) pdf Math. Biosci. 160, 191-213, 1999. 
Poincare's stability conditions for quasi-periodic solutions. (with J. S. Muldowney) pdf Canadian Quart. Appl Math. 6, 367-381, 1998. 
A geometric approach to global stability problem.
(with J. S. Muldowney)
pdf SIAM J. Math. Anal. 27, 1070-1083, 1996.
Global stability for the SEIR model in epidemiology. 
(with J. S. Muldowney)
pdf Math. Biosci. 125, 155-164, 1995.
Phase asymptotic flows, Poincare's stability condition and the existence of stable limit cycles. (with J. S. Muldowney) pdf J. Differential Equations 124, 425-448, 1996.
Dulac criteria for autonomous systems having an invariant affine manifold. pdf J. Math. Anal. Appl. 199, 374-390, 1996.
Lower bounds for the Hausdorff dimension of attractors. 
(with J. S. Muldowney)
reprint J. Dyn. & Diff. Equat. 7, 457-469, 1995.
Bendixson's criterion for autonomous systems having an invariant linear subspace. pdf Rocky Mountain J. Math. 25, 351-363, 1995.
On R. A. Smith's autonomous convergence theorem. 
(with J. S. Muldowney)
pdf Rocky Mountain J. Math. 25, 365-379, 1995.
On Bendixson's criterion. (with J. S. Muldowney) pdf J. Differential Equations 106, 27-39, 1993.

6. General Dynamical Systems

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Mechanisms for stable coexistence in an insect community, (with M. Fan and B. Zhang) pdf Math. Biosci. Eng. 7, 603 - 622, 2010.
Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion. (with M. Mei, J. So, and S. Shen) pdf Proc. Roy. Soc. Edinburgh Sect. A 134, 579-594, 2004.
Diffusion-driven instability in reaction-diffusion systems. (with L. Wang) pdf J. Math. Anal. Appl. 254, 138-153, 2001.
A generalization of the Milloux-Hartman theorem for nonlinear systems. (with J. Karsai and J. R. Graef) reprint Communications in difference equations (Poznan, 1998), 203--213, Gordon and Breach, Amsterdam, 2000.
A criterion for stability of matrices. (with L. Wang) pdf J. Math. Anal. Appl. 225, 249-264, 1998.