SCIENCE & EDUCATION

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1 Bauman Moscow State Technical University, Moscow, Russia

The paper considers a mathematical model describing dynamics of the cell population system consisting of normal and abnormal stem cells. It offers a technique to provide the estimates and a distribution of the model parameters on the basis of limited sampling of experimental data. The model is a non-linear system of ordinary differential equations of the first order to determine the changing populations of normal and abnormal cells. The number of populations serves as the model variables. The model takes into account the limited resources and is nonlinear regarding the model variables, but it is linear with respect to unknown parameters and is considered in the domain where both populations evolve. To solve the problem of parametric identification of mathematical model was obtained its discrete analogue. The task of identifying vectors of the model parameters was divided into two independent sub-tasks. The first stage estimated parameters, which determined dynamics of the normal cell population evolution. The second one estimated parameters defining dynamics of the abnormal cell population evolution. The features of the proposed technique are to select a family of disjoint templates that allows us to have both the point estimates and the posterior distributions of the mathematical model parameters for small samples. Relationships are obtained to allow us to calculate point estimates and construct a probability density function of the vectors of the model parameters using the limited samples of experimental data. When building a distribution of the model parameters a Bayesian approach and a Jeffreys theory of invariance were used. The obtained distributions of parameters are the generalized t-distribution.

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