Evaluation of the Accuracy of Approximations of the Differential Growth Model Using the Logistic Model

We consider a general model of population growth given by a differential equation. Assuming that the right-hand side of the equation is unknown, we approximate the model under consideration using the classical logistic model. We establish two inequalities that evaluate the accuracy of the approximation: (a) Upper bounds for the uniform proximity of trajectories in bounded time intervals. (b) An upper bound for the difference between asymptotically stable states. The results are new and original. To obtain them, we used the contractions technique, well-known in the theory of differential equations.