On the existence and exponential attractivity of a unique positive almost periodic solution to an impulsive hematopoiesis model with delays

TL;DR

This paper proves the existence and exponential stability of a unique positive almost periodic solution in a delayed impulsive hematopoiesis model, using contraction mapping and impulsive delay inequalities, supported by numerical validation.

Contribution

It introduces a new approach employing impulsive delay inequalities to establish the existence and stability of solutions in hematopoiesis models with delays and impulses.

Findings

Existence of a unique positive almost periodic solution

Global exponential attractivity of the solution

Numerical example confirming theoretical results

Abstract

In this paper, a generalized model of hematopoiesis with delays and impulses is considered. By employing the contraction mapping principle and a novel type of impulsive delay inequality, we prove the existence of a unique positive almost periodic solution of the model. It is also proved that, under the proposed conditions in this paper, the unique positive almost periodic solution is globally exponentially attractive. A numerical example is given to illustrate the effectiveness of the obtained results.