This paper presents a new generalized model of hematopoiesis with multiple time-varying delays. The main purpose of this paper is to study the existence and the global exponential stability of the positive pseudo almost periodic solutions, which are more general and complicated than periodic and almost periodic solutions. Under suitable assumptions, and by using fixed point theorem, sufficient conditions are given to ensure that all solutions of this model converge exponentially to the positive pseudo almost periodic solution for the considered model. These results improve and extend some known relevant results.

As we all know, many phenomena in nature have oscillatory character and their mathematical models have led to the introduction of certain classes of functions to describe them. For example, the pseudo almost periodic functions are the natural generalization of the concept of almost periodicity. These are functions on the real numbers set that can be represented uniquely in the form

Motivated by the above discussions, in this paper, we consider the existence, uniqueness, and global exponential stability of positive pseudo almost periodic solutions of (

Throughout this paper, for

Due to the biological interpretation of model (

In this section, some lemmas and definitions will be presented, which are of importance in proving our main results in Section

In this paper,

Let

We denote by

Let

Set

Let

Assume that

Let

Every solution

Suppose that there exist two positive constants

This Lemma can be proven in a similar way to that in Lemma 2.2 of [

We finally show that

Suppose that

Consider

For any

Since

Under the assumptions of Theorem

By Theorem

Let

It follows from Lemma

We consider the Lyapunov functional

We claim that

In this section, we present an example to check the validity of the results we obtained in the previous sections.

Numerical solution

We remark that the results in [

The author declares no conflict of interests. She also declares that she has no financial or personal relationships with other people or organizations that can inappropriately influence her work. There are no professional or other personal interests of any nature or kind in any product, service, and/or company that could be construed as influencing the position presented in, or the review of, this paper.

The author would like to express the sincere appreciation to the editor and reviewer for their helpful comments in improving the presentation and quality of the paper. In particular, the author expresses the sincere gratitude to Professor Zhibin Chen and Professor Bingwen Liu for the helpful discussion when this revision work was being carried out. This work was supported by the National Natural Science Foundation of China (Grant no. 11201184), the Natural Scientific Research Fund of Zhejiang Provincial of P.R. China (Grant nos. Y6110436 and LY12A01018), and the Natural Scientific Research Fund of Zhejiang Provincial Education Department of P.R. China (Grant no. Z201122436).