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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]

The APOBEC3 (A3) genes encode cytidine deaminase proteins with potent antiviral and anti-retroelement activity. This locus is characterized by duplication, recombination, and deletion events that gave rise to the seven A3s found in primates. These include three single deaminase domain A3s (A3A, A3C, and A3H) and four double deaminase domain A3s (A3B, A3D, A3F, and A3G). The most potent of the A3 proteins against HIV-1 is A3G. However, it is not clear if double deaminase domain A3s have a generalized functional advantage to restrict HIV-1. In order to test whether superior restriction factors could be created by genetically linking single A3 domains into synthetic double domains, we linked A3C and A3H single domains in novel combinations. We found that A3C/A3H double domains acquired enhanced antiviral activity that is at least as potent, if not better than, A3G. Although these synthetic double domain A3s package into budding virions more efficiently than their respective single domains, this does not fully explain their gain of antiviral potency. The antiviral activity is conferred both by cytidine-deaminase dependent and independent mechanisms, with the latter correlating to an increase in RNA binding affinity. T cell lines expressing this A3C-A3H super restriction factor are able to control replicating HIV-1ΔVif infection to similar levels as A3G. Together, these data show that novel combinations of A3 domains are capable of gaining potent antiviral activity to levels similar to the most potent genome-encoded A3s, via a primarily non-catalytic mechanism. Author summary: Antiviral genes are encoded by all organisms to help protect them from viral infections, including proteins encoded by primates to protect them from viruses similar to HIV-1. These antiviral proteins are also called "restriction factors". Some restriction factors are broadly acting, while others are very specific. During the course of evolution, some of these genes have expanded into multiple copies and rearranged in different versions to give them new activities. In this paper, we validated the hypothesis that one particular antiviral gene family, called the APOBEC3 family, has the capability of making novel combinations of antiviral human genes with as great, or greater, potency against HIV-1 as the most potent natural member of this family. By combining parts of the APOBEC3 proteins into novel combinations, we created potent antiviral versions that act through a mechanism distinct from existing APOBEC3 proteins. [ABSTRACT FROM AUTHOR]

Reducing the pool of HIV-1 reservoirs in patients is a must to achieve functional cure. The most prominent HIV-1 cell reservoirs are resting CD4 + T cells and brain derived microglial cells. Infected microglial cells are believed to be the source of peripheral tissues reseedings and the emergence of drug resistance. Clearing infected cells from the brain is therefore crucial. However, many characteristics of microglial cells and the central nervous system make extremely difficult their eradication from brain reservoirs. Current methods, such as the "shock and kill", the "block and lock" and gene editing strategies cannot override these difficulties. Therefore, new strategies have to be designed when considering the elimination of brain reservoirs. We set up an original gene suicide strategy using latently infected microglial cells as model cells. In this paper we provide proof of concept of this strategy. [ABSTRACT FROM AUTHOR]

In the literature, several mathematical models have been formulated and developed to describe the within-host dynamics of either human immunodeficiency virus (HIV) or human T-lymphotropic virus type I (HTLV-I) monoinfections. In this paper, we formulate and analyze a novel within-host dynamics model of HTLV-HIV coinfection taking into consideration the response of cytotoxic T lymphocytes (CTLs). The uninfected CD 4 + T cells can be infected via HIV by two mechanisms, free-to-cell and infected-to-cell. On the other hand, the HTLV-I has two modes for transmission, (i) horizontal, via direct infected-to-cell touch, and (ii) vertical, by mitotic division of active HTLV-infected cells. It is well known that the intracellular time delays play an important role in within-host virus dynamics. In this work, we consider six types of distributed-time delays. We investigate the fundamental properties of solutions. Then, we calculate the steady states of the model in terms of threshold parameters. Moreover, we study the global stability of the steady states by using the Lyapunov method. We conduct numerical simulations to illustrate and support our theoretical results. In addition, we discuss the effect of multiple time delays on stability of the steady states of the system. [ABSTRACT FROM AUTHOR]

In this paper, a model of HIV infection taking into account cell-free and cell-to-cell transmissions is investigated under latency. The viral production rate of infectious CD4 T cells and the activation rate of latently infected CD4 T cells play a major role in the evolution of the disease. A system of nonlinear differential equations is derived to capture the dynamics and systematically analyzed thanks to the spectral theory of dynamical systems and a Routh-Hurwitz criterion. In particular, numerical simulations will be performed in order to extract the critical epidemiological features of the solution. [ABSTRACT FROM AUTHOR]

HIV preferentially infects activated CD4+ T cells. Current antiretroviral therapy cannot eradicate the virus. Viral infection of other cells such as macrophages may contribute to viral persistence during antiretroviral therapy. In addition to cell-free virus infection, macrophages can also get infected when engulfing infected CD4+ T cells as innate immune sentinels. How macrophages affect the dynamics of HIV infection remains unclear. In this paper, we develop an HIV model that includes the infection of CD4+ T cells and macrophages via cell-free virus infection and cell-to-cell viral transmission. We derive the basic reproduction number and obtain the local and global stability of the steady states. Sensitivity and viral dynamics simulations show that even when the infection of CD4+ T cells is completely blocked by therapy, virus can still persist and the steady-state viral load is not sensitive to the change of treatment efficacy. Analysis of the relative contributions to viral replication shows that cell-free virus infection leads to the majority of macrophage infection. Viral transmission from infected CD4+ T cells to macrophages during engulfment accounts for a small fraction of the macrophage infection and has a negligible effect on the total viral production. These results suggest that macrophage infection can be a source contributing to HIV persistence during suppressive therapy. Improving drug efficacies in heterogeneous target cells is crucial for achieving HIV eradication in infected individuals. [ABSTRACT FROM AUTHOR]

Aim and Objective: HIV (Human Immunodeficiency Virus) has been reported to weaken the immune system by binding to CD4+ receptor of T lymphocytes, thereby making the affected individual to become more susceptible to several microbial infections leading to life threatening problems. Recent literature indicate there is promsing advancement in identifying drug targets through CD4+ receptor binding capabilities with its ligand. The main purpose of this paper was to study the various molecular interactions of HIV to other molecules like receptors CD4+ and also co-receptors like CCR5 and CXCR4. Materials and Required: The molecules are going to be modeled by using software known as Swiss PDB viewer. The first objective is to get the FASTA sequence from the NCBI website. Then we need to paste the sequence onto the Swiss PDB viewer. Conclusion: The requierd protein/molecule is modeled. We are going to follow this method to obtain templates and modles for the following molecukles: HIV, GP120, CCR5 and CXCR4. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a multidelayed in‐host HIV model to represent the interaction between human immunodeficiency virus and immune response. One delay was considered to incorporate the time required by the virus for various intracellular events to make a host cell productively infective, and the second delay was introduced to take into account the time required for adaptive immune system to respond against infection. We extensively analyzed this multidelayed model analytically and numerically. We show that delay may have both destabilizing and stabilizing effects even when the system contains a single immune response delay. It happens when there exists two sequences of critical values of this delay. If the system starts with stable state in absence of delay, then the smallest value of these critical delays causes instability and the next higher value causes stability. The system may also show stability switching for different values of the virus replication factor. These results demonstrate the possible reasons of intrapatients and interpatients variability of CD4+ T cells and virus counts in HIV‐infected patients. [ABSTRACT FROM AUTHOR]

In this paper, applying both Lyapunov function techniques and monotone iterative techniques,we establish new sufficient conditions under which the infected equilibrium of an HIV pathogenesis model with cure rate is globally asymptotically stable. By giving an explicit expression for eventual lower bound of the concentration of susceptible CD4C T cells, we establish an affirmative partial answer to the numerical simulations investigated in the recent paper [Liu, Wang, Hu and Ma, Global stability of an HIV pathogenesis model with cure rate, Nonlinear Analysis RWA (2011) 12: 2947-2961]. Our monotone iterative techniques are applicable for the small and large growth rate in logistic functions for the proliferation rate of healthy and infected CD4+ T cells. [ABSTRACT FROM AUTHOR]

Recent studies demonstrate that resource competition is an essential component of T-cell proliferation in HIV progression, which can contribute instructively to the disease development. In this paper, we formulate an age-structured within-host HIV model, in the form of a hyperbolic partial differential equation (PDE) for infected target cells coupled with two ordinary differential equations for uninfected T-cells and the virions, to explore the effects of both the T-cell competition and viral shedding variations on the viral dynamics. The basic reproduction number is derived for a general viral production rate which determines the local stability of the infection-free equilibrium. Two special forms of viral production rates, which are extensively investigated in previous literature, the delayed exponential distribution and a step function rate, are further investigated, where the original system can be reduced into systems of delay differential equations. It is confirmed that there exists a unique positive equilibrium for two special viral production rates when the basic reproduction number is greater than one. However, the model exhibits the phenomenon of backward bifurcation, where two positive steady states coexist with the infection-free equilibrium when the basic reproduction number is less than one. [ABSTRACT FROM AUTHOR]

Estimating the time since infection (TI) in newly diagnosed HIV-1 patients is challenging, but important to understand the epidemiology of the infection. Here we explore the utility of virus diversity estimated by next-generation sequencing (NGS) as novel biomarker by using a recent genome-wide longitudinal dataset obtained from 11 untreated HIV-1-infected patients with known dates of infection. The results were validated on a second dataset from 31 patients. Virus diversity increased linearly with time, particularly at 3rd codon positions, with little inter-patient variation. The precision of the TI estimate improved with increasing sequencing depth, showing that diversity in NGS data yields superior estimates to the number of ambiguous sites in Sanger sequences, which is one of the alternative biomarkers. The full advantage of deep NGS was utilized with continuous diversity measures such as average pairwise distance or site entropy, rather than the fraction of polymorphic sites. The precision depended on the genomic region and codon position and was highest when 3rd codon positions in the entire pol gene were used. For these data, TI estimates had a mean absolute error of around 1 year. The error increased only slightly from around 0.6 years at a TI of 6 months to around 1.1 years at 6 years. Our results show that virus diversity determined by NGS can be used to estimate time since HIV-1 infection many years after the infection, in contrast to most alternative biomarkers. We provide the regression coefficients as well as web tool for TI estimation. unfortunately, they only distinguish between recent and long-term infections (concentration of HIV-1-specific antibodies) or are imprecise (immune status as measured by levels of CD4+ T-lymphocytes and viral sequence diversity measured by polymorphisms in Sanger sequences). In this paper, we show that recent advances in sequencing technologies, i.e. the development of next generation sequencing, enable significantly more precise determination of the time since HIV-1 infection, even many years after the infection event. This is a significant advance which could translate into more effective HIV-1 prevention [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze an HIV dynamics model. The model can be seen as a generalization of many HIV dynamics models presented in the literature since it incorporates (i) two classes of target cells, CD4+ T cells and macrophages, (ii) two types of infected cells, short-lived infected cells and the long-lived chronically infected cells, (iii) intracellular discrete delays, (iv) reverse transcriptase inhibitors (RTIs) drugs with different drug efficacies on CD4+T cells and macrophages. The incidence rate of infection is represented by a general function. A bifurcation parameter, known as the basic reproduction number, R0 is derived. We established a set of conditions on the general function which are sufficient to determine the global dynamics of the model. Using Lyapunov functionals and LaSalle's invariance principle, the global asymptotic stability of the two equilibria of the model is obtained. An example is presented and some numerical simulations are conducted in order to illustrate the dynamical behavior. [ABSTRACT FROM AUTHOR]

In this paper, we construct an HIV infection model which includes latent infection, logistic growth for healthy CD4 T-cells, and antiretroviral therapy. We obtain the global asymptotic stability of the uninfected equilibrium by constructing a Lyapunov function, and we give a sufficient condition for the local asymptotic stability of the infected equilibrium. We also use the latin hypercube sampling technique to identify the key parameters in determining the stability of the infected equilibrium. By numerical simulations, we observe that the model without logistic growth would underestimate the number of infectious virions, while the model without latent infection would overestimate the number of infectious virions. [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]

During early human immunodeficiency virus (HIV) infection multiple CD8+ T cell responses are elicited almost simultaneously. These responses exert strong selective pressures on different parts of HIV’s genome, and select for mutations that escape recognition and are thus beneficial to the virus. Some studies reveal that the later these escape mutations emerge, the more slowly they go to fixation. This pattern of escape rate decrease(ERD) can arise by distinct mechanisms. In particular, in large populations with high beneficial mutation rates interference among different escape strains –an effect that can emerge in evolution with asexual reproduction and results in delayed fixation times of beneficial mutations compared to sexual reproduction– could significantly impact the escape rates of mutations. In this paper, we investigated how interference between these concurrent escape mutations affects their escape rates in systems with multiple epitopes, and whether it could be a source of the ERD pattern. To address these issues, we developed a multilocus Wright-Fisher model of HIV dynamics with selection, mutation and recombination, serving as a null-model for interference. We also derived an interference-free null model assuming initial neutral evolution before immune response elicitation. We found that interference between several equally selectively advantageous mutations can generate the observed ERD pattern. We also found that the number of loci, as well as recombination rates substantially affect ERD. These effects can be explained by the underexponential decline of escape rates over time. Lastly, we found that the observed ERD pattern in HIV infected individuals is consistent with both independent, interference-free mutations as well as interference effects. Our results confirm that interference effects should be considered when analyzing HIV escape mutations. The challenge in estimating escape rates and mutation-associated selective coefficients posed by interference effects cannot simply be overcome by improved sampling frequencies or sizes. This problem is a consequence of the fundamental shortcomings of current estimation techniques under interference regimes. Hence, accounting for the stochastic nature of competition between mutations demands novel estimation methodologies based on the analysis of HIV strains, rather than mutation frequencies. [ABSTRACT FROM AUTHOR]

Based on some important biological meanings, we propose a class of HIV infection models incorporating both classical cell-free virus diffusion and direct cell-to-cell transmission. According to recent studies, the direct cell-to-cell transfer of HIV is a significantly more efficient mode of retroviral dissemination. In the first part of our analysis, we show that our model possesses non-negative solutions. Then, we derive sufficient conditions for the asymptotic stability of equilibriums. The analytical solutions are verified by simulation results. At the end of the paper, some important conclusions are given. [ABSTRACT FROM AUTHOR]

This paper analyzes the main trend of the development of acquired immunodeficiency syndrome (AIDS) vaccines in recent years. Designing an HIV-1 vaccine that provides robust protection from HIV-1 infection remains a challenge despite many years of effort. Therefore, we describe the receptor binding domain of gp120 as a target for developing AIDS vaccines. And we recommend some measures that could induce efficiently and produce cross-reactive neutralizing antibodies with high binding affinity. Those measures may offer a new way of the research and development of the potent and broad AIDS vaccines. [ABSTRACT FROM AUTHOR]

In this paper, we study the global properties of two mathematical models which describe the interaction of the human immunodeficiency virus (HIV) with two classes of target cells, CD4+ T cells and macrophages. The incidence rate of virus infection is given by the Crowley-Martin functional response. The first model has two types of discrete delays while the second one incorporates two types of distributed delays to describe the time needed for infection of cell and virus replication. The basic reproduction number R0 is identified which completely determines the global dynamics of the models. By constructing suitable Lyapunov functionals, we have proven that if R0 ≤ 1 then the uninfected steady state is globally asymptotically stable (GAS), and if R0 > 1 then the infected steady state exists and it is GAS. [ABSTRACT FROM AUTHOR]

In this paper, we study the global analysis of virus dynamics models with discrete delay and with distributed delay. The models describe the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages. The incidence rate of virus infection is given by the Beddington-DeAngelis functional response. The models have two types of discrete time delay or distributed delay describing the time needed for infection of cell and virus replication. The basic reproduction number R0 is identified which completely determines the global dynamics of the models. By constructing suitable Lyapunov functionals, we have proven that if R0 ≤ 1 then the uninfected steady state is globally asymptotically stable (GAS), and if R0 > 1 then the infected steady state exists and it is GAS. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we sought to identify the CD4+ T-cell dynamics in the course of HIV infection in response to continuous and intermittent intravenous courses of interleukin-2 (IL-2), the principal cytokine responsible for progression of CD4+ T-lymphocytes from the G1 to the S phase of the cell cycle. Based on multivariate regression models, previous literature has concluded that the increase in survival of CD4+ T-cell appears to be the critical mechanism leading to sustained CD4+ T-cell levels in HIV-infected patients receiving intermittent IL-2 therapy. Underscored by comprehensive mathematical modeling, a major finding of the present work is related to the fact that, rather than due to any increase in survival of CD4+ T-cells, the expressive, selective and sustained CD4+ T-cell expansions following IL-2 administration may be related to the role of IL-2 in modulating the dynamics of Fas-dependent apoptotic pathways, such as activation-induced cell death (AICD) or HIV-specific apoptotic routes triggered by viral proteins. [Copyright &y& Elsevier]

The holy grail for HIV-1 vaccine researchers is to develop an efficacious vaccine, a goal that would be aided by defining a correlate of protection from infection. Recently, the authors of two papers have come one step closer to this goal with the definition of a correlate of survival following simian immunodeficiency virus (SIV) infection: the preservation of memory CD4+ T cells during acute infection. Both of these research groups show that vaccination can prevent the initial immune devastation caused by SIV infection and that this correlates with survival following SIV challenge. Here, we highlight the significance of these two recent papers in light of the urgent need to produce an efficacious HIV vaccine and discuss several crucial issues that must be addressed before the correlate can be used in human clinical trials. [Copyright &y& Elsevier]

In this paper, we introduce ordinary and delay differential equations to describe the interactions between a malignant tumour and the immune systemin vivoin the presence of human immunodeficiency virus (HIV) infection of CD4+T-cells. In the delay model, we take into account the time lags required by the healthy effector cell components to recognize the pathogens and tumour cells. The models consist of four populations: tumour cells, healthy effector cells (CD4+T-cells), effector cells infected by HIVs and free viral particles. The presence of delay term in the model leads to a notable increase in the complexity of the observed behaviour. We investigate the qualitative behaviour of the models and find the conditions that guarantee the asymptotic stability of the steady states. Numerical simulations are provided to illustrate and extend the theoretical results. The obtained results are consistent with the real phenomena and give a better understanding of cancer immunity and viral oncogenesis. [ABSTRACT FROM PUBLISHER]

During an infection, HIV experiences strong selection by immune system T cells. Recent experimental work has shown that MHC escape mutations form an important pathway for HIV to avoid such selection. In this paper, we study a model of MHC escape mutation. The model is a predator-prey model with two prey, composed of two HIV variants, and one predator, the immune system CD8 cells. We assume that one HIV variant is visible to CD8 cells and one is not. The model takes the form of a system of stochastic differential equations. Motivated by well-known results concerning the short life-cycle of HIV intrahost, we assume that HIV population dynamics occur on a faster time scale then CD8 population dynamics. This separation of time scales allows us to analyze our model using an asymptotic approach. Using this model we study the impact of an MHC escape mutation on the population dynamics and genetic evolution of the intrahost HIV population. From the perspective of population dynamics, we show that the competition between the visible and invisible HIV variants can reach steady states in which either a single variant exists or in which coexistence occurs depending on the parameter regime. We show that in some parameter regimes the end state of the system is stochastic. From a genetics perspective, we study the impact of the population dynamics on the lineages of an HIV sample taken after an escape mutation occurs. We show that the lineages go through severe bottlenecks and that in certain parameter regimes the lineage distribution can be characterized by a Kingman coalescent. Our results depend on methods from diffusion theory and coalescent theory. [ABSTRACT FROM AUTHOR]

Abstract: The strategies of structured treatment interruptions (STIs) of antiretroviral therapies have been proposed for clinical management of HIV infected patients, but clinical studies on STIs failed to achieve a consistent conclusion for this strategy. To evaluate the STI strategies, in particular, CD4+ T cell count-guided STIs, and explain these controversial conclusions from different clinical studies, in this paper we propose to use piecewise HIV virus dynamic models to quantitatively explore the STI strategies and investigate their dynamic behaviors. Our analysis results indicate that CD4+ T cell counts can be maintained above a safe level using the STI with a single threshold or a threshold window. Numerical simulations show that the CD4+ T cell counts either fluctuate or approach a stable level for a patient, depending on the prescribed upper or lower threshold values. In particular, the CD4+ T cell counts can be stabilized at a desired level if the threshold policy control is applied. The durations of drug-on and drug-off are very sensitive to the prescribed upper or lower threshold levels, which possibly explains why the on–off strategy with fixed schedule or an STI strategy with frequent switches are associated with the high rate of failure. Our findings suggest that it is critical to carefully choose the thresholds of CD4+ T cell count and individualize the STIs for each individual patient based on initial CD4+ T cell counts. [Copyright &y& Elsevier]

While antiretroviral drugs can drive HIV to undetectably low levels in the blood, eradication is hindered by the persistence of long-lived, latently infected memory CD4 T cells. Immune activation therapy aims to eliminate this latent reservoir by reactivating these memory cells, exposing them to removal by the immune system and the cytotoxic effects of active infection. In this paper, we develop a mathematical model that investigates the use of immune activation strategies while limiting virus and latent class rebound. Our model considers infection of two memory classes, central and transitional CD4 T cells and the role that general immune activation therapy has on their elimination. Further, we incorporate ways to control viral rebound by blocking activated cell proliferation through anti proliferation therapy. Using the model, we provide insight into the control of latent infection and subsequently into the long term control of HIV infection. [ABSTRACT FROM AUTHOR]

Background: In highly antiretroviral-experienced patients with a multidrug-resistant human immunodeficiency virus (HIV) infection, recommended regimens should preferentially contain 3 active components, including a ritonavir-boosted protease inhibitor (PI/r). Tipranavir/r (TPV/r), a non-peptidic PI, has been specifically developed for patients resistant to the usual antiretroviral classes including PIs. This paper discusses the role of TPV/r in patients experiencing multiple PI resistance. Methods: Virological, immunological, and safety outcomes were collected between 2003 and 2007 at 7 clinical units. Virus resistance assessment was based on 3 different genotypic tests. The 207 patients evaluated had previously received nucleoside reverse transcriptase inhibitors (NRTIs) and PIs. Results: The main drugs co-administered with TPV/r were 1 or 2 NRTIs associated, in half of the patients, with enfuvirtide. After 12 weeks, viral load was <50 copies/ml in 38% of the patients (44% with enfuvirtide), while median CD4 counts had increased from 150 to 250 cells/mm3. Genotypic testing suggested that most of the patients had viruses susceptible to TPV. Lipid and transaminase levels were slightly modified, and less than 10% of treatment discontinuations were due to gastrointestinal events. Conclusion: A regimen including TPV/r associated with at least 1 active component is a valuable option in highly ARV-experienced patients with multi-resistance to the usual ARV classes including PIs. [ABSTRACT FROM AUTHOR]

The major pathway for HIV internalization in CD4+ T cells has been thought to be the direct fusion of virus and cell membranes, because the cell surface is the point of entry of infectious particles. However, the exact contribution of endocytic pathways to the infection of CD4+ T lymphocytes is unknown, and the mechanisms involved in endocytosis of HIV particles are unclear. Recent evidence suggests that endocytosis of cell-free and cell-associated virus particles could lead to effective virus entry and productive infections. Such observations have, in turn, spurred a debate on the relevance of endosomal entry as a mechanism of escape from the immune system and HIV entry inhibitors. In this paper, we review the endocytosis of HIV and discuss its role in HIV infection and pathogenesis. [ABSTRACT FROM AUTHOR]

Cortical F-actin plays important roles during HIV-1 infection. A recent paper in Cell highlights the involvement of F-actin in enhancing dendritic cell (DC)-mediated HIV-1 infection of T cells. Such a critical mechanism of HIV-1 trans -enhancement between human DCs and T cells had not been analyzed in molecular detail before this work. [ABSTRACT FROM AUTHOR]

The discovery of HIV-1 as the cause of AIDS was one of the major scientific achievements during the last century. Here the events leading to this discovery are reviewed with particular attention to priority and actual contributions by those involved. Since I would argue that discovering HIV was dependent on the previous discovery of the first human retrovirus HTLV-I, the history of this discovery is also re-examined. The first human retroviruses (HTLV-I) was first reported by Robert C. Gallo and coworkers in 1980 and reconfirmed by Yorio Hinuma and coworkers in 1981. These discoveries were in turn dependent on the previous discovery by Gallo and coworkers in 1976 of interleukin 2 or T-cell growth factor as it was called then. HTLV-II was described by Gallo's group in 1982. A human retrovirus distinct from HTLV-I and HTLV-II in that it was shown to have the morphology of a lentivirus was in my mind described for the first time by Luc Montagnier in an oral presentation at Cold Spring Harbor in September of 1983. This virus was isolated from a patient with lymphadenopathy using the protocol previously described for HTLV by Gallo. The first peer reviewed paper by Montagnier's group of such a retrovirus, isolated from two siblings of whom one with AIDS, appeared in Lancet in April of 1984. However, the proof that a new human retrovirus (HIV-1) was the cause of AIDS was first established in four publications by Gallo's group in the May 4th issue of Science in 1984. [ABSTRACT FROM AUTHOR]

Background: Cytotoxic T cell (CTL) cross-reactivity is believed to play a pivotal role in generating immune responses but the extent and mechanisms of CTL cross-reactivity remain largely unknown. Several studies suggest that CTL clones can recognize highly diverse peptides, some sharing no obvious sequence identity. The emerging realization in the field is that T cell receptors (TcR) recognize multiple distinct ligands. Principal Findings: First, we analyzed peptide scans of the HIV epitope SLFNTVATL (SFL9) and found that TCR specificity is position dependent and that biochemically similar amino acid substitutions do not drastically affect recognition. Inspired by this, we developed a general model of TCR peptide recognition using amino acid similarity matrices and found that such a model was able to predict the cross-reactivity of a diverse set of CTL epitopes. With this model, we were able to demonstrate that seemingly distinct T cell epitopes, i.e., ones with low sequence identity, are in fact more biochemically similar than expected. Additionally, an analysis of HIV immunogenicity data with our model showed that CTLs have the tendency to respond mostly to peptides that do not resemble self-antigens. Conclusions: T cell cross-reactivity can thus, to an extent greater than earlier appreciated, be explained by amino acid similarity. The results presented in this paper will help resolving some of the long-lasting discussions in the field of T cell cross-reactivity. [ABSTRACT FROM AUTHOR]

We present a review and comparison of several recent differential equations models of treatment of HIV-1 infection. We seek to clarify the role of the natural anti-HIV immune response and determine its effect upon optimal treatment schemes. In this paper, we consider systems in which treatment is expressed as a forcing function, as well as those in which we determine optimal treatment via control theoretic techniques. The primary goal of this study is to compare treatment schemes for systems in which a natural nonconstant immune response of the patient is considered explicitly with those that consider implicitly a constant non-specific immune response. We find that when the natural immune response can be boosted sufficiently, drug levels may not need to be as high as previously supposed. This implies that a treatment scenario in which intervals of drug treatment are alternated with some form of immune-boosting therapy may be highly beneficial in terms of reducing toxicity to the patient. Additionally, in developing countries where HIV infection is widespread and sufficient funds are not available to supply rigourous drug regimens, the implications of these models are profound, as they suggest methods of treating HIV at a minimal cost. [ABSTRACT FROM AUTHOR]

In this paper, neglecting the effects of free virus, we consider a simple model of cell-to-cell spread of HIV-1. We discuss the impact of the CD8+ cell non-cytotoxic anti-viral response (CNAR) and cytotoxic T lymphocyte (CTL) activity on infection by HIV-1. Two types of models are considered: the ordinary differential equation (ODE) model and the discrete time delay differential equation (DDE) system. The steady states of the ODE model are globally asymptotically stable respectively under two threshold criteria. In the DDE model, the global stability of the infected steady state of the ODE model becomes only ultimately stable. Moreover, at a certain interval of the time delay, the DDE model will produce Hopf bifurcation or periodic solutions. The introduction of CTL and CNAR will change the values of these steady states and induce fluctuations in the cell concentration. It also affects the critical value of the time delay and is of utility in the interpretation of typical HIV-dynamics data resulting from clinical trials. The DDE model produces sustained infective oscillations in some real parameter values, which is different from the result of the similar cell-free viral spread model with delay. [ABSTRACT FROM AUTHOR]

The requirements for the eradication of HIV in infected individuals are unknown. Intermittent administration of the immune activator interleukin-2 (IL-2) in combination with highly-active anti-retroviral therapy (HAART) has been suggested as an effective strategy to realize long-term control of HIV replication in vivo . However, potential latent virus reservoirs are considered to be a major impediment in achieving this goal. In this paper, a new mathematical model is designed and used to monitor the interactions between HIV, CD4+ T-cells, CD8+ T-cells, productively infected and latently infected CD4+ T-cells, and to evaluate therapeutic strategies during the first 3 years of HIV infection. The model shows that current anti-HIV therapies, including intermittent IL-2 and HAART, are insufficient in achieving eradication of HIV. However, it suggests that the HIV eradication may indeed be theoretically feasible if such therapy is administered continuously (without interruption) under some specified conditions. These conditions may realistically be achieved using an agent (such as a putative anti-HIV vaccine) that brings about a concomitant increase in the proliferation of HIV-specific CD4+ T- and CD8+ T-cells and the differentiation of CD8+ T-cells into anti-HIV cytotoxic T lymphocytes (CTLs). [ABSTRACT FROM AUTHOR]

Linked Content This article is linked to Lattanzi paper. To view this article visit https://doi.org/10.1111/apt.14994. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the qualitative behavior of HIV dynamics models with immune impairment. The HIV particles infect both CD4+ T cells and macrophages. Both latently and actively infected cells are incorporated into the models. The models consider multiple discrete or distributed delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The existence and global stability of the steady states are determined by the basic reproduction number. The global stability analysis of the steady states is performed using Lyapunov method. We solve the system of delay differential equations numerically to support the theoretical results. [ABSTRACT FROM AUTHOR]