Identication Parameters in a Biological Model of Immune Competition : Global Optimization and Kriging Method


  • Lekbir Afraites* University Sultan Moulay Slimane FST - Beni Mellal
  • Abdelghani Bellouquid University Cadi Ayyad ENSA - Safi



In this work, we study the problem of identifying parameters in the
model of immune competition developed in ([1], [2]). Specically, we use
the approach of the inverse problem which will allow the identication of
parameters from measurements of densities of two populations of cells in
the proliferation case. The reformulation of the given nonlinear identica-
tion problem was considered as a parametric optimization problem using
the Least Square criterion. In this work, a design procedure for global ro-
bust optimization is developed using Kriging [4] and global optimization
approaches [3]. Robustness is determined by the Kriging model to reduce
the number of real functional calculations of Least Square criterion. The
technical of the global optimization methods is adopted to determine the
global robust optimum of a surrogate model.



[1] A. Bellouquid, M. Delitala, Modelling Complex Biological Systems: Akinetic Theory Approch, Birkuser, Boston, Basel, Berlin (2006).

[2] N. Bellomo, A. Bellouquid and M. Delitala, Mathematical Topics onthe Modelling Complex Multicellular Systems and Tumor Immune CellsCompetition, Mathematical Models and Methods in Applied SciencesVol. 14, No. 11 , 1683-1733 (2004).

[3] Donald R.Jones, Matthias Schonlau and William J.Welch EcientGlobal Optimization of Expensive Black-Box Functions Journal ofGlobal Optimization 13:455-492 (1998).

[4] L. Afraites, J. Hazart, P. Schiavone, Application of the Kriging methodto the reconstruction of ellipsometric signature, Microelectronic Engi-neering, Vol. 86, issue 4-6, pp. 1033-1035 (2009).






Conference Contributions