Practical identifiability of mathematical models of biomedical processes

Abstract

The paper is devoted to a numerical study of the uniqueness and stability of problems of
determining the parameters of dynamical systems arising in pharmacokinetics, immunology,
epidemiology, sociology, etc. by incomplete measurements of certain states of the system at fixed
time. Significance of parameters difficult to measure is very high in many areas, as their definition
will allow physicians and doctors to make an effective treatment plan and to select the optimal set
of medicines. Due to the fact that the problems under consideration are ill-posed, it is necessary to
investigate the degree of ill-posedness before its numerical solution. One of the most effective ways
is to study the practical identifiability of systems of nonlinear ordinary differential equations that
will allow us to establish a set of identifiable parameters for further numerical solution of inverse
problems. The paper presents three methods for investigating practical identifiability: the Monte
Carlo method, the matrix correlation method, and the confidence intervals method. It is presented
two mathematical models of the pharmacokinetics of the C-peptide and unidentifiable parameters
were determined using the PottersWheel and AMIGO software packages. The similarity of results
is shown, and also the advantages of each of the packages are demonstrated. This investigation
will allow us to construct a regularized unique solution of the inverse problem.