Novel techniques in parameter estimation for fractional dynamical models arising from biological systems

Authors:
F. Liu;K. Burrage
Affiliations:
Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia;Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia and Oxford University Computing Laboratory and OCISB, Oxford University, Oxford, OX1 3QD, U ...
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

In recent years, both parameter estimation and fractional calculus have attracted a considerable interest. Parameter estimation of the fractional dynamical models is a new topic. In this paper, we consider novel techniques for parameter estimation of fractional nonlinear dynamical models in systems biology. First, a computationally effective fractional Predictor-Corrector method is proposed for simulating fractional complex dynamical models. Second, we convert the parameter estimation of fractional complex dynamical models into a minimization problem of the unknown parameters. Third, a modified hybrid simplex search (MHSS) and a particle swarm optimization (PSO) is proposed. Finally, these techniques are applied to a dynamical model of competence induction in a cell with measurement error and noisy data. Some numerical results are given that demonstrate the effectiveness of the theoretical analysis.