Jiaxu Li

Arizona State University

Department of Mathematics 

 

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Research interests

Publications

Glucose-insulin 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 beta-cells 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), 1763-1785.  (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 de-differentiation network, J. Comput. Biol., Jul;20(7):524-39 (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), 1524-1548. (This paper is selected as SIAM Nugget, http://connect.siam.org/toward-an-artficial-pancreas-math-modeling-and-diabetes-control/) (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), 128--137. 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: Glucose-Insulin 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 mini-review, Discrete Contin. Dynam. Systems, B. 12:2 (2009), 401--414. (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, 261--544. (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), 41-58. (reprint)

[11] H. Wang, J. Li and Y. Kuang, Enhanced modeling of the glucose-insulin system and its applications in insulin therapies, J. Biol. Dynamics, 3 (1) (2009), 22-38. (reprint)

[10] H. Wang, J. Li and Y. Kuang, Mathematical modeling and qualitative analysis of insulin therapies, Math. Biosci. 210 (2007) 17-33. (reprint)

[9] J. Li and  Y. Kuang, Analysis of a model of the glucose-insulin regulatory system with two delays, SIAM J. Appl. Math., 67 (3), 757-776, 2007. (reprint)

[8] J. Li,  Y. Kuang and C. Mason, Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two time delays, J. of Theor. Biol., 242, 722-735  (2006). (reprint)

[7] A. Makroglou, J. Li and Y. Kuang, Mathematical models and software tools for the glucose-insulin regulatory system and diabetes:  an overview, Applied Numerical Mathematics, 56, 559-573 (2006). (reprint)

[6] J. Li, Y. Kuang and B. Li, Analyses of IVGTT glucose-insulin interaction models with  time delay, Discrete Contin. Dynam. Systems, B. 1, 103-124(2001). (reprint)

[5] X. Chen and J. Li, On the qualitative behaviour of solutions of the Lienard equation, Ann. Diff. Equa., 12 (1996), 3, 267-279.

[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, 6-12.

[3] J. Li, On the equivalency of oscillation between the unforced and the forced Lienard equation, Acta Sci. Natur. Univ. Heilongjiang, 7 (1990), 1, 23-26.

[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, 162-170. (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, 559-565.
 

 

 

Recent Talks

  • A novel approach for estimation of delay differential equation models, The 9th AIMS International Conference, Orlando, FL, July 1-5, 2012.
  • Antiapoptotic effect of insulin on beta-cells, The 9th AIMS International Conference, Orlando, FL, July 1-5, 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 glucose-insulin 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, UT-ORNL-KBRIN Bioinformatics Summit 2010, Lake Barkley State Resort Park, Cadiz, KY, March 19-21, 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. 9-12, 2009.
  • A few models in glucose-insulin regulatory system, Northeast Normal University, Changchun China, June 29, 2009.
  • A few models in glucose-insulin regulatory system, International Workshop on Reaction-Diffusion Models and Mathematical Biology, June 24-27, 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 14-17, 2009.
  • A few models in glucose-insulin 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 24-26, 2008.
  • Mathematical models in glucose-insulin 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 18-21, 2008.
  • Modeling the glucose-insulin regulation system: towards to artificial pancreas, SS38, The 7th AIMS International Conference, Arlington, TX, May 18-21, 2008.
  • Modeling glucose-insulin regulatory system with two-time delays, AMS Western Section Meeting, Claremont, CA, May 3-4, 2008.
  • Modeling and Analysis of Glucose-Insulin 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, July-Aug., 2006.
  • Modeling glucose-insulin regulatory system with explicit time delays, Dept. of Mathematics and Statistics, University of North Florida, Jacksonville, FL, Feb., 2006.
  • Modeling glucose-insulin 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 glucose-insulin 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