The growth model with a logistic hazard rate of the resource exhaustion

Anastasiia A. Usova, Alexander M. Tarasyev

N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of RAS

Abstract: The paper studies a probabilistic interpretation of the dynamic model of a resource-dependent economy with phase constraints. It is shown that the main model factor is one of the important indicators of the reliability theory, which is a hazard rate determined by a random time moment when the model constraints are violated. If a hazard function is given, then the distribution of the random variable can be uniquely established. In addition, all the main factors of the model can be calculated through the hazard rate and its integral analogue. The paper proposes to consider a logistic function as a candidate for the hazard function and shows the ways for identifying its unknown parameters. The obtained results are illustrated by numerical experiments.

Keywords: dynamic growth models, phase constraints, reliability theory, hazard rate (function).

UDC: 517.977, 519.873
BBK: 22.18

Received: 15.11.2025
Revised: 06.12.2025
Accepted: 15.12.2025