Probabilistic determination of stability for a delay-differential model of the glucose-insulin dynamical system

Journal of Biological Systems

Volumn 7, Issue 2, 1999, Pages 131-144

  De Gaetano, A ^a,c   Arino, O ^b  

^a CNR   (Italy)

^b CNRS   (France)

^c CATHOLIC UNIVERSITY   (Italy)

Author keywords

Delay; Differential equations; Dynamical systems; Glucose; Probability; Stability

Indexed keywords

EID: 0346491861     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339099000115     Document Type: Article

References (9)

1. Bergman R. N., Ider Y. Z., Bowden C. R. and Cobelli C., "Quantitative estimation of insulin sensitivity", Am. J. Physiol. 236 (1979) pp. E667-E677.
2. Blythe S. P., Nisbet R. M. and Gurney W. S. C., "Instability and complex dynamic behavior in population models with long time delays", Theor. Pop. Biol. 2 (1982) pp. 147-176.
3. De Gaetano A., Castagneto M., Mingrone G., Coleman W. P., Sganga G., Tataranni P. A., Gangeri G. and Greco A. V., "PC-based differential model fitting as a support for clinical research," Int. J. Clin. Monit. Comput. 11 (1994) pp. 35-41.
4. Dunkel G., "Single-species model for population growth depending on past history", Lecture Notes in Mathematics 60 (1968) pp. 92-99.
5. Hale J. K., Ordinary Differential Equations (Wiley Interscience, New York, 1969).
6. MacDonald N., "Biological delay systems: linear stability theory" (Cambridge Univ. Press, Cambridge, 1989).
7. Pacini G. and Bergman R. N., "MINMOD: a computer program to calculate insulin sensitivity and pancreatic responsivity from the frequently sampled intravenous glucose tolerance test", Comput. Methods Programs Biomed. 23 (1986) pp. 113-122.
8. Press W. H., Flannery B. P., Teukolsky S. A. and Vetterling W. T., Numerical Recipes in C. The Art of Scientific Computing (Cambridge Univ. Press, New York, 1988).
9. Volterra V., Theorie Mathematique de la Lutte Pour la Vie (Paris, Gauthier-Villars, 1931).