Research interests
Publications
Glucoseinsulin system
Mathematical biology
Useful links

Refereed
Publications
(Please note that the publishers are the copyright holders of the
published articles)
[22] C. Hu, J. Li and J. D. Johnson, Modeling the distribution of
insulin in pancreas, in review.
[21] A. Makroglou, I. Karaoustas, J. Li
and Y. Kuang, A review on delay differential
equation models in diabetes modeling, II: the insulin therapies and the
intracellular activities of betacells case, in review.
[20]
X. Song, M. Huang and J. Li, Modeling impulsive insulin delivery in
insulin pump with delays, SIAM J. Appl. Math., 74:6
(2014), 17631785. (reprint)
[19] M.
Wang, J. Li, G. Lim and J. D. Johnson, Is dynamic autocrine
insulin signaling possible? Amathematical model
predicts picomolar concentrations of extracellular monomeric insulin with human pancreatic islets, PLoS ONE, 8:6 (2013), e64860.
DOI:10.1371/journal.pone.0064860 (reprint)
[18] J.
Kim, J. Li, S. G. Venkatesh, D. S. Darling, G. A.
Rempala, Model discrimination in dynamic molecular systems: Application to
parotid dedifferentiation network, J. Comput.
Biol., Jul;20(7):52439 (2013). DOI:
10.1089/cmb.2011.0222 (reprint)
[17] M. Huang, J. Li, X. Song and H. Guo, Modeling impulsive injections of insulin: towards arti_cial pancreas, SIAM J. Appl. Math., 72:5 (2012), 15241548. (This
paper is selected as SIAM Nugget, http://connect.siam.org/towardanartficialpancreasmathmodelinganddiabetescontrol/)
(reprint)
[16] J.
Li, M. Wang, A. De Gaetano, P. Palumbo and S. Panunzi, The range of time delay and the global stability
of the equilibrium for an IVGTT model, Math.
Biosci., 235 (2012), 128137. doi:10.1016/j.mbs.2011.11.005
(available online since Nov. 19, 2011.) (PMID: 22123436.) (reprint)
[15] A. Makroglou, I. Karaoustas, J.
Li, Y. Kuang, Delay differential equation models in
diabetes modeling: a review, EOLSS
encyclopedia, developed under the auspices of UNESCO, Oxford, UK, Chapter
title: GlucoseInsulin Regulatory System, in theme titled: Mathematical
Physiology, edited by: Andrea de Gaetano, Pasquale
Palumbo, 2011.
[14] J.
Li and J. Johnson, Mathematical models of subcutaneous injection of insulin
analogues: a minireview, Discrete Contin. Dynam. Systems, B.
12:2 (2009), 401414. (reprint)
[13]
Yang Kuang, Jiaxu Li, Bingtuan
Li, Urszula Ledzewicz and
Ami Radunskaya, Mathematical
Biology and Medicine, a special issue of Discrete and Continuous Dynamical
Systems, Series B, Vol. 12:2, Sept. 2009, 261544. (contents)
[12] J.
Li and Y. Kuang, Systemically modeling the dynamics
of plasma insulin in subcutaneous injection of insulin analogues for type 1
diabetes, Mathematical Biosciences and Engineering, 6 (1) (2009),
4158. (reprint)
[11] H.
Wang, J. Li and Y. Kuang, Enhanced modeling of the
glucoseinsulin system and its applications in insulin therapies, J. Biol.
Dynamics, 3 (1) (2009), 2238. (reprint)
[10] H.
Wang, J. Li and Y. Kuang, Mathematical modeling and
qualitative analysis of insulin therapies, Math. Biosci.
210 (2007) 1733. (reprint)
[9] J.
Li and Y. Kuang,
Analysis of a model of the glucoseinsulin regulatory system with two delays,
SIAM J. Appl. Math., 67 (3), 757776, 2007. (reprint)
[8] J. Li, Y. Kuang
and C. Mason, Modeling the glucoseinsulin regulatory system and ultradian insulin secretory
oscillations with two time delays, J. of Theor.
Biol., 242, 722735 (2006).
(reprint)
[7] A. Makroglou, J. Li and Y. Kuang, Mathematical models and software tools for the
glucoseinsulin regulatory system and diabetes: an overview, Applied
Numerical Mathematics, 56, 559573 (2006). (reprint)
[6] J. Li, Y. Kuang and B. Li, Analyses of
IVGTT glucoseinsulin interaction models with time
delay, Discrete Contin. Dynam.
Systems, B. 1, 103124(2001). (reprint)
[5] X.
Chen and J. Li, On the qualitative behaviour
of solutions of the Lienard equation, Ann. Diff.
Equa., 12 (1996), 3, 267279.
[4] J.
Li, Existence of limit cycles for the system dx/dt = φ(y)  F(x), dy/dt = g(x), Acta
Sci. Natur. Univ. Heilongjiang, 9
(1992), 2, 612.
[3] J.
Li, On the equivalency of oscillation between the unforced and the
forced Lienard equation, Acta
Sci. Natur. Univ. Heilongjiang, 7
(1990), 1, 2326.
[2] J.
Li, H. Fan, T. Jiang and X. Chen, Qualitative analysis of differential
equations for a class of multimolecular reaction models,
J. Biomath., 5 (1990), 2, 162170. (abstract).
[1] X. Chen, J. Li and H.
Fan, Harmonic solutions of the equation x''+f(x)x'+g(x)
= p(t), Chin. Ann. Math. Ser. A, 11 (1990), 5, 559565.
Recent Talks
 A novel approach for estimation of delay differential
equation models, The 9th AIMS International Conference, Orlando, FL,
July 15, 2012.
 Antiapoptotic
effect of insulin on betacells, The 9th AIMS International Conference,
Orlando, FL, July 15, 2012.
 Mathematical models in intravenous glucose tolerance
test (IVGTT), University of Science and Technology Beijing (USTB),
Beijing, China, June 13, 2011.
 Mathematical models in intravenous glucose tolerance
test (IVGTT), Xinyang Normal University, Xinyang, China, June 7,
2011.
 Mathematical models in glucoseinsulin regulatory
system, Xinyang Normal University, Xinyang, China, June 7, 2011.
 Modeling scaling insulin concentrations in islet and
insulin distribution in pancreas, International Congress of Mathematical
Biology, Nanjing, China, June 4, 2011.
 Modeling scaling insulin concentrations in islet and
insulin distribution in pancreas, Arizona State University, April 29,
2011.
 Two mathematical models in medicine, Beijing University
of Technology, China, June 21, 2010.
 Some examples in mathematical medicine, University of
Shanghai for Science and Technology, China, June 18, 2010.
 Delay differential equations and its applications,
Beijing University of Technology, China, May 31, 2010.
 Modeling Terminal Differentiation of Mammalian Cells,
UTORNLKBRIN Bioinformatics Summit 2010, Lake Barkley State Resort
Park, Cadiz, KY, March 1921, 2010. (with Douglas Darling.)
 Delay Dependent Conditions for Global Stability of an
Intravenous Glucose Tolerance Test Model, The Second International
Conference on Mathematical Modeling and Analysis of Populations in
Biological Systems, Huntsville, AL, Oct. 912, 2009.
 A few models in glucoseinsulin regulatory system,
Northeast Normal University, Changchun China, June 29, 2009.
 A few models in glucoseinsulin regulatory system,
International Workshop on ReactionDiffusion Models and Mathematical
Biology, June 2427, Harbin, P. R. China.
 Global stability of a model in intravenous glucose
tolerance test, the First Joint Conference of the Society for
Mathematical Biology and the Chinese Society for Mathematical Biology, Hangzhou , P. R. China, June 1417, 2009.
 A few models in glucoseinsulin regulatory system,
Beijing Univeristy of Techonology,
Beijing China, June 19, 2009.
 Mathematical models of the dynamics of insulin
concentration, COBRE, University of Louisville, Louisville, KY, March, 2009.
 Systemically modeling the dynamics
of plasma insulin in subcutaneous injection of insulin analogues for type
1 diabetes, 2008 Fall AMS Sectional Meetings, University of Alabama at
Huntsville, Huntsville, AL, October 2426,
2008.
 Mathematical models in glucoseinsulin regulation
system, University of British Columbia, August, 2008.
 Pharmacokinetical models of subcutaneous injection of insulin
analogues for type 1 diabetes, SS43, The 7th
AIMS International Conference, Arlington, TX, May 1821, 2008.
 Modeling the glucoseinsulin regulation system:
towards to artificial pancreas, SS38, The 7th
AIMS International Conference, Arlington, TX, May 1821, 2008.
 Modeling glucoseinsulin regulatory system with
twotime delays, AMS Western Section Meeting, Claremont, CA, May 34, 2008.
 Modeling and
Analysis of GlucoseInsulin Regulatory System with Explicit Time Delays,
KBRIN Summit, March, 2008. (Poster).
 Modeling the Insulin Analogue Administration for Type
1 Diabetes, DESU Summer Workshop, Delaware State University, Dover, DE, Aug., 2007.
 Mathematical modeling and qualitative analysis of
insulin therapies, DESU Summer Workshop, Delaware State University,
Dover, DE, JulyAug., 2006.
 Modeling glucoseinsulin regulatory system with
explicit time delays, Dept. of Mathematics and Statistics, University of
North Florida, Jacksonville, FL, Feb., 2006.
 Modeling glucoseinsulin metabolic system and insulin
secretory ultradian
oscillations with explicit time delays, DESU Summer Workshop, Delaware
State University, Dover, DE, Aug., 2005.
 Modeling the Ultradian
Oscillations of Insulin Secretion with Two Time Delays, AMS Annual Conference,
Atlanta, GA, Jan., 2005.
 The Dynamics Of Insulin Secretion: Rapid Oscillation
and Ultradian Oscillation, AIMS' Fifth
International Conference on Dynamical Systems and Differential
Equations, Pomona, CA, June, 2004.
 Mathematical models and software for the
glucoseinsulin regulatory system associated with diabetes: An overview,
Third International Conference on the Numerical Solutions of Volterra and Delay Equations, Tempe, AZ, May, 2004.
Software Packages
Please note that the software packages developed by Jiaxu Li are
not commercial software. Users in academic area are welcome to use them, however they may not be readily applicable for
inexperienced users. Interested users can either contact me or wait until I
make them more user friendly.
 Bifurcation Analyzer for DDE
models
 Bifurcation Analyzer for ODE models
