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This paper deals with the problem of identifying parameters in the mathematical model of immune competition developed in [Modelling Complex Biological Systems: A Kinetic Theory Approach, Birkhäuser, Boston, 2006]. More precisely, we use the approach called  inverse problem  to identify the parameters of the model, and we investigate the identifiability as well as the stability of the inverse problem. In numerical analysis, the inverse problem is reformulated as an optimization problem where the variables are the estimated parameters in the model. In our study, the regularized least-squares cost function and the adjoint technique to compute the gradient of the cost function are used. Finally, some numerical tests for parameters identification using synthetic data are presented.

Parameters identification in the mathematical model of immune competition cells