Dynamics of two time delays differential equation model to HIV latent infection

Liu, Huijuan; Zhang, Jia-Fang

doi:10.1016/j.physa.2018.09.087

Cited by 46 publications

(21 citation statements)

References 29 publications

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“…Although antiretroviral therapies have been successful in decreasing the mortality rate in some regions, it is still necessary to increase antiretroviral therapies in other regions. Many HIV/AIDS epidemic models have been proposed to predict and control the spread of the disease (see, e.g., [3,[8][9][10][11] and the references cited therein).…”

Section: Introductionmentioning

confidence: 99%

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

2019

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In recent years, many new definitions of fractional derivatives have been proposed and used to develop mathematical models for a wide variety of real-world systems containing memory, history, or nonlocal effects. The main purpose of the present paper is to develop and analyze a Caputo-Fabrizio fractional derivative model for the HIV/AIDS epidemic which includes an antiretroviral treatment compartment. The existence and uniqueness of the system of solutions of the model are established using a fixed-point theorem and an iterative method. The model is shown to have a disease-free and an endemic equilibrium point. Conditions are derived for the existence of the endemic equilibrium point and for the local asymptotic stability of the disease-free equilibrium point. The results confirm that the disease-free equilibrium point becomes increasingly stable as the fractional order is reduced. Numerical simulations are carried out using a three-step Adams-Bashforth predictor method for a range of fractional orders to illustrate the effects of varying the fractional order and to support the theoretical results.

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Section: Introductionmentioning

confidence: 99%

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

2019

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“…Nowak and Bangham have formulated the basic virus dynamics model that characterizes the dynamics of viruses with susceptible host cells and infected cells. In fact, this model has given opportunities to develop many models that describe the within‐host dynamics of different viruses such as human immunodeficiency virus (HIV), hepatitis B virus (HBV), hepatitis C virus (HCV), and human T‐cell leukemia virus (HTLV) . The basic model presented in Nowak and Bangham has been extended by assuming that the time from the contact of viruses and susceptible cells to the death of the cells is modeled by dividing the process into n short stages I 1 → I 2 →....→ I n as the following:

({, \begin{matrix} left \\ array \dot{S} (t) = ¥ (S (t)) - ℵ_{11} (S (t)) ℵ_{12} (V (t)), \\ array İ_{1} (t) = ℵ_{11} (S (t)) ℵ_{12} (V (t)) - b_{1} ℏ_{1} (I_{1} (t)), \\ array İ_{2} (t) = d_{1} ℏ_{1} (I_{1} (t)) - b_{2} ℏ_{2} (I_{2} (t)), \\ array İ_{3} (t)... \end{matrix})

…”

Section: Introductionmentioning

confidence: 99%

Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

Ełaiw

AlShamrani

2019

Math Methods in App Sciences

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This paper studies an (n+4)-dimensional nonlinear virus dynamics model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, B cells and cytotoxic T lymphocyte (CTL) cells. Both viral and cellular infections have been incorporated into the model. The infectedsusceptible and virus-susceptible infection rates as well as the generation and removal rates of all compartments are described by general nonlinear functions. Five threshold parameters are computed, which insure 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 dynamics 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. KEYWORDS adaptive immune response, global stability, Lyapunov function, multistaged infected cells, viral and cellular infections CLASSIFICATION 34D20; 34D23; 37N25; 92B05

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“…The global stability of delayed virus dynamics models has been studied in several works (see, e.g., [21][22][23][24][25][26][27][28][29][30][31]). HIV dynamics models with latently-infected cells and two time delays were proposed and studied in [32,33].…”

Section: Introductionmentioning

confidence: 99%

Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions

2019

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In this paper, we construct an Human immunodeficiency virus (HIV) dynamics model with impairment of B-cell functions and the general incidence rate. We incorporate three types of infected cells, (i) latently-infected cells, which contain the virus, but do not generate HIV particles, (ii) short-lived productively-infected cells, which live for a short time and generate large numbers of HIV particles, and (iii) long-lived productively-infected cells, which live for a long time and generate small numbers of HIV particles. The model considers five distributed time delays to characterize the time between the HIV contact of an uninfected CD4 + T-cell and the creation of mature HIV. The nonnegativity and boundedness of the solutions are proven. The model admits two equilibria, infection-free equilibrium E P 0 and endemic equilibrium E P 1 . We derive the basic reproduction number R 0 , which determines the existence and stability of the two equilibria. The global stability of each equilibrium is proven by utilizing the Lyapunov function and LaSalle’s invariance principle. We prove that if R 0 < 1 , then E P 0 is globally asymptotically stable, and if R 0 > 1 , then E P 1 is globally asymptotically stable. These theoretical results are illustrated by numerical simulations. The effect of impairment of B-cell functions, time delays, and antiviral treatment on the HIV dynamics are studied. We show that if the functions of B-cells are impaired, then the concentration of HIV is increased in the plasma. Moreover, we observe that the time delay has a similar effect to drug efficacy. This gives some impression for developing a new class of treatments to increase the delay period and then suppress the HIV replication.

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Dynamics of two time delays differential equation model to HIV latent infection

Cited by 46 publications

References 29 publications

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions

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