On a Logistic Differential Model. Some Applications

Abstract

In this article we will consider the possibility of approximating the input function s(t) (the nutrient supply for cell growth) of the form s(t)=1/(1+mt)exp(-mt)) where m>0 is parameter.We prove upper and lower estimates for the one--sided Hausdorff approximation of the shifted Heaviside function by means of the general solution of the differential equation y'(t)=ky(t)s(t) with y(t_0)=y_0.We will illustrate the evolution of the solution y(t) for approximating and modelling of three data sets: i) ''data on the development of the Drosophila melanogaster population'', published by Pearl in 1920, ii) dataStormIdentifications (Storm worm was one of the most biggest cyber threats of 2008, and ''cancer data''.Numerical examples using CAS Mathematica, illustrating our results are given.