Modeling the Dynamics of Age-Structured Polycyclic Population of Biological Cells on the Parameterized Set of Algebraic Functions

Abstract

We use the analytical approach and numerical modeling to analyze the dynamics of the population of biological cells based on the polycyclic age-structured model. We reduce the initial-boundary-value problem for transport equation to the Volterra integral equation of the second kind and solve it by infinite convergent series. For the initial-boundary-value problem for transport equation, we obtain an explicit two-layer numerical difference scheme of the second order of approximation with respect to time and the first one with respect to age with explicit recurrent formula for the integral boundary condition. We consider the set of main biological parameters of the system as a set of parameterized algebraic functions with compact domain of definition. The parameter identification problem is solved for approximate analytical solutions for the data of dried biomass of hop plant observed for 3 years. Since the maximum relative error of deviation of the simulated curves from the points of experimental data is less than 11%, we conclude that polycyclic age-structured cell population model is efficient to solve applied problems in biological systems.