Stability of within host HTLV-I/HIV-1 co-infection in the presence of macrophages

The main target of both human immunodeficiency virus type 1(HIV-1)and human Tlymphotropic virus type I(HTLV-I)is the CD4+T cell which is considered the key player in the immune system.Moreover,HIV-1 has another target that is the macrophages.The present paper aims to formulate and develop a mathematical model to analyze the interaction of two viruses,HIV-1 and HTLV-I with the immune system.We determine a bounded domain for the concentrations of the model's compartments.We discuss the dynamical behavior of the model and analyze the existence and stability of the system's steady states.The global asymptotic stability of all steady states is proven by utilizing the Lyapunov method.We also demonstrate the dynamical behavior of the system numerically.The significant impact of macrophages on the HTLV-I/HIV-1 co-infection dynamics is discussed.Our developed model will contribute to the understanding of HTLV-I/HIV-1 co-infection dynamics and help to choose different treatment strategies against HIV-1 and HTLV-I.

Impact of adaptive immune response and cellular infection on delayed virus dynamics with multi-stages of infected cells

In this investigation,we propose and analyze a virus dynamics model with multi-stages of infected cells.The model incorporates the effect of both humoral and cell-mediated immune responses.We consider two modes of transmissions,virus-to-cell and cell-to-cell.Multiple intracellular discrete-time delays have been integrated into the model.The incidence rate of infection as well as the generation and removal rates of all compartments are described by general nonlinear functions.Wc derive five threshold parameters which determine the existence of the equilibria of the model under consideration.A set of conditions on the general functions has been established which is sufficient to investigate the global stability of the five equilibria of the model.The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle’s invariance principle.The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.

Modeling and stability analysis of HIV/HTLV-I co-infection

Human immunodeficiency virus(HIV)and human T-Iymphotropic virus type I(HTLV-I)are two retroviruses that infect the susceptible CD4^(+)T cells.It is known that HIV and HTLV-I have in common a way of transmission through direct contact with certain body fluids related to infected individuals.Therefore,it is not surprising that a mono-infected person with one of these viruses can be co-infected with the other virus.In the literature,a great number of mathematical models has been presented to describe the within-host dynamics of HIV or HTLV-I mono-infection.However,the within-host dynamics of HIV/HTLV-I co-infection has not been modeled.In this paper,we develop a new within-host HIV/HTLV-I co-infection model.The model includes the impact of Cytotoxic T lymphocytes(CTLs)immune response,which is important to control the progression of viral co-infection.The model describes the interaction between susceptible CD4^(+)T cells,silent HIV-infected cells,active HIV-infected cells,silent HTLV-infected cells,Tax-expressing HTLV-infected cells,free HIV particles,HIV-specific CTLs and HTLV-specific CTLs.We first show the nonnegativity and boundedness of the model’s solutions and then we calculate all possible equilibria.We derive the threshold parameters which govern the existence and stability of all equilibria of the model.We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle’s invariance principle.We have presented numerical simulations to illustrate the effectiveness of our main results.In addition,we discuss the effect of HTLV-I infection on the HIV-infected patients and vice versa.