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In this paper, we investigate a stochastic human immunodeficiency virus (HIV) model with logistic growth and Ornstein-Uhlenbeck process, which is used to describe the pathogenesis and transmission dynamics of HIV in the population. We first validate that the stochastic system has a unique global solution with any initial value. Then we use a novel Lyapunov function method to establish sufficient conditions for the existence of a stationary distribution of the system, which shows the coexistence of all CD4+ T cells and free viruses. Especially, under some mild conditions which are used to ensure the local asymptotic stability of the quasi-chronic infection equilibrium of the stochastic system, we obtain the specific expression of covariance matrix in the probability density around the quasi-chronic infection equilibrium of the stochastic system. In addition, for completeness, we also obtain sufficient criteria for elimination of all infected CD4+ T cells and free virus particles. Finally, several examples together with comprehensive numerical simulations are conducted to support our analytic results. [ABSTRACT FROM AUTHOR]

This paper presents and analyzes two mathematical models for the human immunodeficiency virus type-1 (HIV-1) infection with Cytotoxic T Lymphocyte cell (CTL) immune impairment. These models describe the interactions between healthy CD 4 + T cells, latently and actively infected cells, HIV-1 particles, and CTLs. The healthy CD 4 + T cells might be infected when they make contact with: (i) HIV-1 particles due to virus-to-cell (VTC) contact; (ii) latently infected cells due to latent cell-to-cell (CTC) contact; and (iii) actively infected cells due to active CTC contact. Distributed time delays are considered in the second model. We show the nonnegativity and boundedness of the solutions of the systems. Further, we derive basic reproduction numbers ℜ 0 and ℜ ˜ 0 , that determine the existence and stability of equilibria of our proposed systems. We establish the global asymptotic stability of all equilibria by using the Lyapunov method together with LaSalle's invariance principle. We confirm the theoretical results by numerical simulations. The effect of immune impairment, time delay and CTC transmission on the HIV-1 dynamics are discussed. It is found that weak immunity contributes significantly to the development of the disease. Further, we have established that the presence of time delay can significantly decrease the basic reproduction number and then suppress the HIV-1 replication. On the other hand, the presence of latent CTC spread increases the basic reproduction number and then enhances the viral progression. Thus, neglecting the latent CTC spread in the HIV-1 infection model will lead to an underestimation of the basic reproduction number. Consequently, the designed drug therapies will not be accurate or sufficient to eradicate the viruses from the body. These findings may help to improve the understanding of the dynamics of HIV-1 within a host. [ABSTRACT FROM AUTHOR]

In this paper, we establish and analyze a stochastic human immunodeficiency virus model with both virus-to-cell and cell-to-cell transmissions and Ornstein–Uhlenbeck process, in which we suppose that the virus-to-cell infection rate and the cell-to-cell infection rate satisfy the Ornstein–Uhlenbeck process. First, we validate that there exists a unique global solution to the stochastic model with any initial value. Then, we adopt a stochastic Lyapunov function technique to develop sufficient criteria for the existence of a stationary distribution of positive solutions to the stochastic system, which reflects the strong persistence of all CD4+ T cells and free viruses. In particular, under the same conditions as the existence of a stationary distribution, we obtain the specific form of the probability density around the quasi-chronic infection equilibrium of the stochastic system. Finally, numerical simulations are conducted to validate these analytical results. Our results suggest that the methods used in this paper can be applied to study other viral infection models in which the infected CD4+ T cells are divided into latently infected and actively infected subgroups. [ABSTRACT FROM AUTHOR]

Much is known about the natural history of syphilis; however, less is known about the immune response against it, and even less is known about people living with HIV (PLWH). Due to the lack of an animal model to study host-pathogen interactions, it remains unclear how the host eliminates the bacteria. Here, we attempt to elucidate the immune response against infection by summarizing all the reported data in a systematic review. We found that only seven papers included PLWH, and they did not accurately describe the immune response against Treponema pallidum since only lymphopenia was reported upon coinfection. On the other hand, at least sixteen papers described the host-pathogen interaction in individual cell populations. Using this information, we established the kinetics of the immune response against syphilis and hypothesized how CD4+ T cells, such as Th17 and T rex cells, worsen the progression of the disease in PLWH through their hallmark cytokines, IL-10 and IL-17, and how these two cytokines may play important roles as biomarkers. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors of a multiple delayed HIV-1 infection model which describes the interactions of humoral, cytotoxic T lymphocyte (CTL) immune responses, and two modes of transmission that are the classical virus-to-cell infection and the direct cell-to-cell transmission are investigated. The model incorporates three delays, including the delays of cell infection, virus production and activation of immune response. We first prove the well-posedness of the model, and calculate the biological existence of equilibria and the reproduction numbers, which contain virus infection, humoral immune response, CTL immune response, CTL immune competition, and humoral immune competition. Further, the threshold conditions for the local and global stability of the equilibria for infection-free, immune-free, antibody response, CTL response, and interior are established by utilizing linearization method and the Lyapunov functionals. The existence of Hopf bifurcation with immune delay as a bifurcation parameter is investigated by using the bifurcation theory. Numerical simulations are carried out to illustrate the theoretical results and reveal the effects of some key parameters on viral dynamics. [ABSTRACT FROM AUTHOR]

In several publications, the dynamical system of HIV and HTLV mono-infections taking into account diffusion, as well as latently infected cells in cellular transmission has been mathematically analyzed. However, no work has been conducted on HTLV/HIV co-infection dynamics taking both factors into consideration. In this paper, a partial differential equations (PDEs) model of HTLV/HIV dual infection was developed and analyzed, considering the cells' and viruses' spatial mobility. CD 4 + T cells are the primary target of both HTLV and HIV. For HIV, there are three routes of transmission: free-to-cell (FTC), latent infected-to-cell (ITC), and active ITC. In contrast, HTLV transmits horizontally through ITC contact and vertically through the mitosis of active HTLV-infected cells. In the beginning, the well-posedness of the model was investigated by proving the existence of global solutions and the boundedness. Eight threshold parameters that determine the existence and stability of the eight equilibria of the model were obtained. Lyapunov functions together with the Lyapunov–LaSalle asymptotic stability theorem were used to investigate the global stability of all equilibria. Finally, the theoretical results were verified utilizing numerical simulations. [ABSTRACT FROM AUTHOR]

Latently infected CD 4 + T cells represent one of the major obstacles to HIV eradication even after receiving prolonged highly active anti-retroviral therapy (HAART). Long-term use of HAART causes the emergence of drug-resistant virus which is then involved in HIV transmission. In this paper, we develop mathematical HIV models with staged disease progression by incorporating entry inhibitor and latently infected cells. We find that entry inhibitor has the same effect as protease inhibitor on the model dynamics and therefore would benefit HIV patients who developed resistance to many of current anti-HIV medications. Numerical simulations illustrate the theoretical results and show that the virus and latently infected cells reach an infected steady state in the absence of treatment and are eliminated under treatment whereas the model including homeostatic proliferation of latently infected cells maintains the virus at low level during suppressive treatment. Therefore, complete cure of HIV needs complete eradication of latent reservoirs. [ABSTRACT FROM AUTHOR]

The human immunodeficiency virus (HIV) interacts with the immune cells within the human body, where the environment is uncertain and noisy. Stochastic models can successfully encapsulate the effect of such a noisy environment compared to their deterministic counterparts. The human immune system is complex but well-coordinated with various immune cells like C D 4 + T cells, dendritic cells, and cytotoxic T-lymphocyte (CTL) cells, among many others. The CTL can kill the antigenic cells after its recognition. However, the efficacy of CTL in removing the infected C D 4 + T cells is progressively compromised in HIV-infected individuals. This paper considers a noise-induced HIV-immune cell interaction model with immune impairment. A multiplicative white noise is introduced in the infection rate parameter to represent the fluctuations around the average value of the rate parameter as a causative effect of the noise. We analyzed the deterministic and stochastic models and prescribed sufficient conditions for infection eradication and persistence. It is determined under what parametric restrictions the asymptotic solutions of the noise-induced system will be a limiting case of the deterministic solutions. Simulation results revealed that the solutions of the deterministic system either converge to a CTL-dominated interior equilibrium or a CTL-free immunodeficient equilibrium, depending on the initial values of the system. Stochastic analysis divulged that higher noise might be helpful in the infection removal process. The extinction time of infected C D 4 + T cells for some fixed immune impairment gradually decreases with increasing noise intensity and follows the power law. [ABSTRACT FROM AUTHOR]

In recent decades, AIDS has been one of the main challenges facing the medical community around the world. Due to the large human deaths of this disease, researchers have tried to study the dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition to clinical trials. In this paper, we study a new mathematical model in which the dynamics of CD 4 + T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional structure for the first time. The kernel of these new fractal-fractional operators is of the generalized Mittag-Leffler type. From an analytical point of view, we first derive some results on the existence theory and then the uniqueness criterion. After that, the stability of the given fractal-fractional system is reviewed under four different cases. Next, from a numerical point of view, we obtain two numerical algorithms for approximating the solutions of the system via the Adams-Bashforth method and Newton polynomials method. We simulate our results via these two algorithms and compare both of them. The numerical results reveal some stability and a situation of lacking a visible order in the early days of the disease dynamics when one uses the Newton polynomial. [ABSTRACT FROM AUTHOR]

HIV-1 establishes a persistent proviral reservoir by integrating into the genome of infected host cells. Current antiretroviral treatments do not target this persistent population of proviruses which include latently infected cells that upon treatment interruption can be reactivated to contribute to HIV-1 rebound. Deep sequencing of persistent HIV proviruses has revealed that greater than 90% of integrated HIV genomes are defective and unable to produce infectious virions. We hypothesized that intragenic elements in the HIV genome support transcription of aberrant HIV-1 RNAs from defective proviruses that lack long terminal repeats (LTRs). Using an intact provirus detection assay, we observed that resting CD4+ T cells and monocyte-derived macrophages (MDMs) are biased towards generating defective HIV-1 proviruses. Multiplex reverse transcription droplet digital PCR identified env and nef transcripts which lacked 5' untranslated regions (UTR) in acutely infected CD4+ T cells and MDMs indicating transcripts are generated that do not utilize the promoter within the LTR. 5'UTR-deficient env transcripts were also identified in a cohort of people living with HIV (PLWH) on ART, suggesting that these aberrant RNAs are produced in vivo. Using 5' rapid amplification of cDNA ends (RACE), we mapped the start site of these transcripts within the Env gene. This region bound several cellular transcription factors and functioned as a transcriptional regulatory element that could support transcription and translation of downstream HIV-1 RNAs. These studies provide mechanistic insights into how defective HIV-1 proviruses are persistently expressed to potentially drive inflammation in PLWH. Author summary: People living with HIV establish a persistent reservoir which includes latently infected cells that fuel viral rebound upon treatment interruption. However, the majority of HIV-1 genomes in these persistently infected cells are defective. Whether these defective HIV genomes are expressed and whether they contribute to HIV associated diseases including accelerated aging, neurodegenerative symptoms, and cardiovascular diseases are still outstanding questions. In this paper, we demonstrate that acute infection of macrophages and resting T cells is biased towards generating defective viruses which are expressed by DNA regulatory elements in the HIV genome. These studies describe an alternative mechanism for chronic expression of HIV genomes. [ABSTRACT FROM AUTHOR]

Human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that infect the susceptible CD 4 + 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 CD 4 + 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. [ABSTRACT FROM AUTHOR]

• Two numerical methods are developed for solving the fractional-order HIV-1 infection model of CD4 + T-cells. • Two method (Bessel matrix method and Bessel quasilinearization method) are based on the novel Bessel polynomials. • Error and convergence analysis are studied. • Numerical applications and comparisons show that methods are effective. • In the comparison of the two methods used, the Bessel-QLM method gives better results. In this paper, two numerical methods based on the novel Bessel polynomials are developed to solve the fractional-order HIV-1 infection model of CD 4 + T-cells considering the impact of antiviral drug treatment. In first of these methods, by using the Bessel polynomial and collocation points, we transform the HIV problem into a system of nonlinear algebraic equations. And this method, which is the method of direct solution is called as Bessel matrix method. The second method, which is called the Bessel-QLM method converts firstly HIV problem to a sequence of linear equations by using the technique of quasilinearization and then the reduced problem is solved by the direct Bessel matrix method. Error and convergence analysis are studied for the Bessel method. Finally, the applications are made on the numerical examples and also the numerical results are compared with the results of other available techniques. It is observed from applications that the presented results are better than the results of other existing methods and also the Bessel-QLM method is more efficient than the direct Bessel method. [ABSTRACT FROM AUTHOR]