HTLV/HIV Dual Infection: Modeling and Analysis

Ahmed M Elaiw,Noura H Alshamrani

doi:10.3390/math9010051

Abstract

Human T-lymphotropic virus type I (HTLV-I) and human immunodeficiency virus (HIV) are two famous retroviruses that share similarities in their genomic organization, and differ in their life cycle as well. It is known that HTLV-I and HIV have in common a way of transmission via direct contact with certain body fluids related to infected patients. Thus, it is not surprising that a single-infected person with one of these viruses can be dually infected with the other virus. In the literature, many researchers have devoted significant efforts for modeling and analysis of HTLV or HIV single infection. However, the dynamics of HTLV/HIV dual infection has not been formulated. In the present paper, we formulate an HTLV/HIV dual infection model. The model includes the impact of the Cytotoxic T lymphocyte (CTLs) immune response, which is important to control the dual infection. The model describes the interaction between uninfected CD4+T cells, HIV-infected cells, HTLV-infected cells, free HIV particles, HIV-specific CTLs, and HTLV-specific CTLs. We establish that the solutions of the model are non-negative and bounded. We calculate all steady states of the model and deduce the threshold parameters which determine the existence and stability of the steady states. We prove the global asymptotic stability of all steady states by utilizing the Lyapunov function and Lyapunov–LaSalle asymptotic stability theorem. We solve the system numerically to illustrate the our main results. In addition, we compared between the dynamics of single and dual infections.

Highlights

Human immunodeficiency virus (HIV) infects the human body and causes acquired immunodeficiency syndrome (AIDS), which is one of the deadly diseases
Human T-lymphotropic virus type I (HTLV-I) is an exogenous retrovirus that infects the human body and can lead to two diseases, one of them an inflammatory of the central nervous system known as HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP) and the other an adult T-cell leukemia (ATL)
The rest of the paper is organized as follows: In Section 2, we propose an HTLV/HIV dual infection model

Summary

Introduction

Human immunodeficiency virus (HIV) infects the human body and causes acquired immunodeficiency syndrome (AIDS), which is one of the deadly diseases. The term π1CI represents the death rate of effective HIV-specific CTLs. Human T-lymphotropic virus type I (HTLV-I) is an exogenous retrovirus that infects the human body and can lead to two diseases, one of them an inflammatory of the central nervous system known as HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP) and the other an adult T-cell leukemia (ATL). The terms δY and π2CY denote the death rates of the HTLV-infected cells and HTLV-specific CTLs, respectively This model has been developed and extended in several works which discussed the dynamical behavior. It has been estimated that the HIV single infected patients have more exposure to be dual infected with HTLV-I at a higher rate initiating from 100 to 500 times in comparison with the uninfected peoples [42].

Steady States

Global Stability Analysis

Stability of the Steady States

Initial-1 Initial-2 Initial-3

Comparison Study

Conclusions and Discussions