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

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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, et al.) pdf Infectious Disease Modeling, 2016, http://dx.doi.org/10.1016/j.idm.2016.05.001
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
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 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
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
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
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
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 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
Impacts of migration and immigration on disease transmission dynamics in heterogeneous populations, (with H. Guo) pdf DCDS-B 17, 2413-2430, 2012
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 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 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.
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.
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.
Bifurcation analysis in a neutral differential equation, (with Y. Qu and J. Wei) pdf J. Math. Anal. Appl. 378, 387-402, 2011.
Modeling the effects of carriers on transmission dynamics of infectious diseases, (with D. Kalajdzievska) pdf Math. Biosci. & Eng. 8, 711-722, 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.
Mechanisms for stable coexistence in an insect community, (with M. Fan and B. Zhang) pdf Math. Biosci. Eng. 7, 603 - 622, 2010.
Global dynamics of an in-host viral model with intracellular delays, (with H. Shu) pdf Bull. Math. Bio. 72, 1429-1505, 2010.
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.
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 stability of an epidemic model in a patchy environment, (with Z. Shuai) pdf Canadian Appl. Math. Quaerter. 17, 175-187, 2009.
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 dynamics of a staged-progression model with amelioration for infectious diseases, (with H. Guo) pdf J. Bio. Dyn. 2, 154-168, 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.
Global dynamics of a staged progression model for infectious diseases, (with H. Guo) pdf Math. Biosci. Eng. 3, 513-525, 2006.
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.
Hopf bifurcation analysis for a delayed Nicholson Blowflies equation. (with J. Wei) pdf Nonlinear Analysis 60, 1351-1367, 2005.
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.
Global existence of periodic solutions in a tri-neuron network model with delays. (with J. Wei) pdf Physica D 198, 106-119, 2004.
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.
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.
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.
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.
Diffusion-driven instability in reaction-diffusion systems. (with L. Wang) pdf J. Math. Anal. Appl. 254, 138-153, 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.
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.
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. 
A criterion for stability of matrices. (with L. Wang) pdf J. Math. Anal. Appl. 225, 249-264, 1998.
Poincare's stability conditions for quasi-periodic solutions. (with J. S. Muldowney) pdf Canadian Quart. Appl Math. 6, 367-381, 1998. 
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.
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.