Mathematical Modeling of Genetic Mechanisms of Cancer

On Solving Biological Problem Based on Functional-Differential Equations of Delay Type With Discrete Experimental Data.

“…and it is required to determine the necessary number of experimental points that allow one to obtain solutions on [t0,t0+10] with an accuracy of 10 -4 . We calculate k from (8). Then equation (10) has the form: An analysis of this equation shows that the minimum number of experimental points that make it possible to obtain a solution on [t0,t0+10h] with an accuracy of 10 -4 , is not more than 48.…”

“…Such equations are functional differential equations with a delayed argument, constructed on the basis of the methods of regulating living systems [3,4]. Functional differential equations of regulatory mechanisms of biological systems are not integrated and obtaining exact solutions is generally impossible [1][2][3][4][5][6][7][8][9]. Using methods of qualitative analysis allows us to identify the general properties of solutions, to determine the characteristic stationary solutions and the existence of periodic solutions.…”

“…Using methods of qualitative analysis allows us to identify the general properties of solutions, to determine the characteristic stationary solutions and the existence of periodic solutions. Solutions can be obtained with the required accuracy based on the implementation of the model on a computer [6][7][8][9][10]. To solve the equations of the regulatory mechanisms of biological systems, it is necessary to set the initial conditions on a segment of length h [11][12][13][14].…”