Research Interests: |
Title | Download | Journal |
Why is it difficult to accurately predict the COVID-19 epidemic? (with W. Roda, M. Varughese, and D. Han) | 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) | Math. Biosci. 308, 27-37, 2019. | |
Efficacy of screening and treatment of latent tuberculosis infection, (with M. Varughese and R. Long) | 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) | 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) | Int. J. Tuberc. Lung Dis., 18(4), 405-412, 2014 |
Title | Download | Journal |
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) | 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) | 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) | 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) | 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) | J. Math. Bio. 65, 181-199, 2012 | |
Joint effects of mitosis and intracellular delay on viral dynamics: two-parameter bifurcation analysis, (with H. Shu) | 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) | 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) | J. Math. Biol. 73, 1774-1793, 2011. | |
Modelling the role of Tax expression in HTLV-I persistence in vivo, (with A. Lim) | Bull. Math. Bio. 73, 3008-3029, 2011. | |
Impact of intracellular delays and target-cell dynamics on in vivo viral infections, (with H. Shu) | 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) | Bull. Math. Bio. 72, 681-696, 2010. | |
Global dynamics of an in-host viral model with intracellular delays, (with H. Shu) | 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) | Math. Biosci. 200, 44-57, 2006. | |
Backward bifurcation in a model for HTLV-I infection of CD4+ T cells. (with H. Gomez-Acevedo) | 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) | 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) | Math. Biosci. 179, 207-217, 2002. |
Title | Download | Journal |
Epidemic models with discrete state structures, (with S. Liu) | 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) | 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) | SIAM J. Appl. Math., 76, 663-687, 2016 | |
Impacts of migration and immigration on disease transmission dynamics in heterogeneous populations, (with H. Guo) | DCDS-B 17, 2413-2430, 2012 | |
Global dynamics of a general class of multistage models for infectious diseases, (with H. Guo and Z. Shuai) | SIAM J. Appl. Math. 72, 261-279, 2012 | |
Global dynamics of a staged-progression model for HIV/AIDS with amelioration, (with H. Guo) | Nonlinear Anal. RWA 12, 2529-2540, 2011. | |
Density dependence in disease incidence and its impacts on transmission dynamics, (with R. de Boer) | Canadian Applied Math. Quarterly 19, 195-218, 2011. | |
Modeling the effects of carriers on transmission dynamics of infectious diseases, (with D. Kalajdzievska) | Math. Biosci. & Eng. 8, 711-722, 2011. | |
Global stability of an epidemic model in a patchy environment, (with Z. Shuai) | Canadian Appl. Math. Quart. 17, 175-187, 2009. | |
Global dynamics of a staged-progression model with amelioration for infectious diseases, (with H. Guo) | J. Bio. Dyn. 2, 154-168, 2008. | |
Global dynamics of a staged progression model for infectious diseases, (with H. Guo) | Math. Biosci. Eng. 3, 513-525, 2006. | |
Global stability in a mathematical model of tuberculosis, (with H. Guo) | Can. Appl. Math. Q 14, 185-197, 2006. | |
Global stability in some SEIR models. (with L. Wang) | 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. |
Title | Download | Journal |
Impact of network connectivity on the synchronization and global dynamics of coupled systems of differential equations, (with P. Du) | Physica D, 287, 32-42, 2014 | |
Global Lyapunov functions and a hierarchical control scheme for networks of robotic agents, (with J. Maidens) | American Control Conference (ACC), 4050-4055, 2013 | |
Global-stability problem for coupled systems of differential equations on networks, (with Z. Shuai) | J. Differential Equations 248, 1-20, 2010. | |
Global stability of multi-group epidemic models with distributed delays, (with Z. Shuai and C. Wang) | 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) | 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) | Canadian Appl. Math. Quaert. 14, 259-284, 2006. |
Title | Download | Journal |
Global Hopf bifurcation analysis of a Nicholson's blowflies equation of neutral type, (with C. Wang and J. Wei) | 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) | DCDS-B, 19, 747-760, 2014 | |
Global Hopf bifurcation analysis of a neuron network model with time delays, (with J. Wei) | Infinite Dimensional Dynamical Systems, Fields Institute Communications, 64, 141-168, 2013 | |
Bifurcation analysis in a neutral differential equation, (with Y. Qu and J. Wei) | J. Math. Anal. Appl. 378, 387-402, 2011. | |
Hopf bifurcation analysis for a delayed Nicholson Blowflies equation. (with J. Wei) | Nonlinear Analysis 60, 1351-1367, 2005. | |
Global existence of periodic solutions in a tri-neuron network model with delays. (with J. Wei) | Physica D 198, 106-119, 2004. | |
Global stability of an SEIS model with recruitment and varying total population. (with M. Fan and K. Wang) | Math. Biosci. 170, 199-208, 2001. | |
Global dynamics of an SEIR model with vertical transmission. (with H. L. Smith and L. Wang) | 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) | J. Differential Equations 168, 295-320, 2000. | |
Global stability for SEIRS models in epidemiology. (with J. S. Muldowney and P. Van den Driessche). | 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) | Math. Biosci. 160, 191-213, 1999. | |
Poincare's stability conditions for quasi-periodic solutions. (with J. S. Muldowney) | Canadian Quart. Appl Math. 6, 367-381, 1998. | |
A geometric approach to global
stability problem.
(with J. S. Muldowney) |
SIAM J. Math. Anal. 27, 1070-1083, 1996. | |
Global stability for the SEIR model
in epidemiology.
(with J. S. Muldowney) |
Math. Biosci. 125, 155-164, 1995. | |
Phase asymptotic flows, Poincare's stability condition and the existence of stable limit cycles. (with J. S. Muldowney) | J. Differential Equations 124, 425-448, 1996. | |
Dulac criteria for autonomous systems having an invariant affine manifold. | 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. | Rocky Mountain J. Math. 25, 351-363, 1995. | |
On R. A. Smith's autonomous convergence
theorem.
(with J. S. Muldowney) |
Rocky Mountain J. Math. 25, 365-379, 1995. | |
On Bendixson's criterion. (with J. S. Muldowney) | J. Differential Equations 106, 27-39, 1993. |
Title | Download | Journal |
Mechanisms for stable coexistence in an insect community, (with M. Fan and B. Zhang) | 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) | Proc. Roy. Soc. Edinburgh Sect. A 134, 579-594, 2004. | |
Diffusion-driven instability in reaction-diffusion systems. (with L. Wang) | 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) | J. Math. Anal. Appl. 225, 249-264, 1998. |