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We propose a class of virus dynamics models with multitarget cells and multiple
intracellular delays and study their global properties. The first model is a 5-dimensional system of nonlinear delay differential equations (DDEs) that describes the interaction of the virus with two classes of target cells. The second model is a (

Nowadays, various types of viruses infect the human body and cause serious and dangerous diseases. Mathematical modeling and model analysis of virus dynamics have attracted the interests of mathematicians during the recent years, due to their importance in understanding the associated characteristics of the virus dynamics and guiding in developing efficient antiviral drug therapies. Several mathematical models have been proposed in the literature to describe the interaction of the virus with the target cells [

A great effort has been made in developing various mathematical models of viral infections with discrete or distributed delays and studying their basic and global properties, such as positive invariance properties, boundedness of the model solutions and stability analysis [^{+} T cells in case of HIV or hepatic cells in case of HCV and HBV). Since the interactions of some types of viruses inside the human body is not very clear and complicated, therefore, the virus may attack more than one class of target cells. Hence, virus dynamics models describing the interaction of the virus with more than one class of target cells are needed. In case of HIV infection, Perelson et al. [^{+} T cells and macrophages. In [

The purpose of this paper is to propose a class of virus dynamics models with multitarget cells and establish the global stability of their steady states. The first model considers the interaction of the virus with two classes of target cells. In the second model, we assume that the virus attacks

In this section, we introduce a mathematical model of virus infection with two classes of target cells. This model can describe the HIV dynamics with two classes of target cells, CD4^{+} T cells and macrophages [

The initial conditions for system (

By the fundamental theory of functional differential equations [

In the following, we establish the nonnegativity and boundedness of solutions of (

Let

From (

To show the boundedness of the solutions, we let

It will be explained in the following that the global behavior of model (

Following the same line as in [

In this section, we prove the global stability of the uninfected and infected steady states of system (

(i) If

(ii) If

(i) We consider a Lyapunov functional

The time derivatives of

(ii) Define a Lyapunov functional as

In this section, we propose a virus dynamics model which describes the interaction of the virus with

The initial conditions for system (

Similar to the previous section, the nonnegativity and the boundedness of the solutions of system (

It is clear that system (

In the following theorem, the global stability of the uninfected and infected steady states of system (

(i) If

(ii) If

(i) Define a Lyapunov functional

To prove (ii), we consider the Lyapunov functional

In this section, we proposed a virus dynamics model which describes the interaction of the virus with

It is clear that system (

In this section, we study the global stability of the uninfected and infected steady states of system (

(i) If

(ii) If

(i) Define a Lyapunov functional

To prove (ii), we consider the Lyapunov functional:

In this paper, we have studied the global properties of a class of virus dynamics models with multitarget cells and multiple delays. First, we have introduced a model with two classes of target cells (CD4^{+} T and macrophages in case of HIV). Then, we have proposed a model describing the interaction of the virus with

^{+}T-cells