Modeling HIV persistence, the latent reservoir, and viral blips

Modeling virus-stimulated proliferation of CD4+ T-cell, cell-to-cell transmission and viral loss in HIV infection dynamics

Human immunodeficiency virus (HIV) can persist in infected individuals despite prolonged antiretroviral therapy and it may spread through two modes: virus-to-cell and cell-to-cell transmissions. Understanding viral infection dynamics is pivotal for elucidating HIV pathogenesis. In this study, we incorporate the loss term of virions, and both virus-to-cell and cell-to-cell infection modes into a within-host HIV model, which also takes into consideration the proliferation of healthy target cells stimulated by free viruses. By constructing suitable Lyapunov function and applying geometric methods, we establish global stability results of the infection free equilibrium and the infection persistent equilibrium, respectively. Our findings highlight the crucial role of the basic reproduction number in the threshold dynamics. Moreover, we use the loss rate of virions as the bifurcation parameter to investigate stability switches of the positive equilibrium, local Hopf bifurcation, and its global continuation. Numerical simulations validate our theoretical results, revealing rich viral dynamics including backward bifurcation, saddle-node bifurcation, and bistability phenomenon in the sense that the infection free equilibrium and a limit cycle are both locally asymptotically stable. These insights contribute to a deeper understanding of HIV dynamics and inform the development of effective therapeutic strategies.

Understanding early HIV-1 rebound dynamics following antiretroviral therapy interruption: The importance of effector cell expansion

Most people living with HIV-1 experience rapid viral rebound once antiretroviral therapy is interrupted; however, a small fraction remain in viral remission for an extended duration. Understanding the factors that determine whether viral rebound is likely after treatment interruption can enable the development of optimal treatment regimens and therapeutic interventions to potentially achieve a functional cure for HIV-1. We built upon the theoretical framework proposed by Conway and Perelson to construct dynamic models of virus-immune interactions to study factors that influence viral rebound dynamics. We evaluated these models using viral load data from 24 individuals following antiretroviral therapy interruption. The best-performing model accurately captures the heterogeneity of viral dynamics and highlights the importance of the effector cell expansion rate. Our results show that post-treatment controllers and non-controllers can be distinguished based on the effector cell expansion rate in our models. Furthermore, these results demonstrate the potential of using dynamic models incorporating an effector cell response to understand early viral rebound dynamics post-antiretroviral therapy interruption.

A novel within-host model of HIV and nutrition

In this paper we develop a four compartment within-host model of nutrition and HIV. We show that the model has two equilibria: an infection-free equilibrium and infection equilibrium. The infection free equilibrium is locally asymptotically stable when the basic reproduction number $ \mathcal{R}_0 < 1 $, and unstable when $ \mathcal{R}_0 > 1 $. The infection equilibrium is locally asymptotically stable if $ \mathcal{R}_0 > 1 $ and an additional condition holds. We show that the within-host model of HIV and nutrition is structured to reveal its parameters from the observations of viral load, CD4 cell count and total protein data. We then estimate the model parameters for these 3 data sets. We have also studied the practical identifiability of the model parameters by performing Monte Carlo simulations, and found that the rate of clearance of the virus by immunoglobulins is practically unidentifiable, and that the rest of the model parameters are only weakly identifiable given the experimental data. Furthermore, we have studied how the data frequency impacts the practical identifiability of model parameters.

Dynamic behaviors of a stochastic virus infection model with Beddington-DeAngelis incidence function, eclipse-stage and Ornstein-Uhlenbeck process

In this paper, we present a virus infection model that incorporates eclipse-stage and Beddington-DeAngelis function, along with perturbation in infection rate using logarithmic Ornstein-Uhlenbeck process. Rigorous analysis demonstrates that the stochastic model has a unique global solution. Through construction of appropriate Lyapunov functions and a compact set, combined with the strong law of numbers and Fatou's lemma, we obtain the existence of the stationary distribution under a critical condition, which indicates the long-term persistence of T-cells and virions. Moreover, a precise probability density function is derived around the quasi-equilibrium of the model, and spectral radius analysis is employed to identify critical condition for elimination of the virus. Finally, numerical simulations are presented to validate theoretical results, and the impact of some key parameters such as the speed of reversion, volatility intensity and mean infection rate are investigated.

Ongoing HIV replication in lymph node sanctuary sites in treated individuals contributes to the total latent HIV at a very slow rate

Lymph nodes (LNs) serve as a sanctuary site for HIV viruses due to the heterogeneous distribution of the antiretrovirals (ARVs) inside the LNs. There is an ongoing debate whether this represents ongoing cycles of viral replication in the LNs or merely residual virus production by latently infected cells. Previous work has claimed that the measured levels of genetic variation in proviruses sampled from the blood were inconsistent with ongoing replication. However, it is not clear what rate of variation is consistent with ongoing replication in small sanctuary sites. In this study, we used a spherically symmetric compartmental ODE model to track the HIV viral dynamics in the LN and predict the contribution of ongoing replication within the LN to the whole-body proviral pool in an ARV-suppressed person living with HIV. This model tracks the reaction-diffusion dynamics of uninfected, actively infected, and latently infected T-cells as well as free virus within the LN parenchyma and the blood, and distinguishes between latently infected cells created before ARV therapy and during ARV therapy. We simulated suppressive therapy beginning in year 5 post-infection. Each LN sanctuary site had a volume of 1 ml, and we considered cases of 1 ml, 30 ml, and 250 ml total volume, which represent a single active sanctuary site, moderate systemic involvement, and involvement of the total lymphoid tissue. Viral load in the blood rapidly dropped and remained below the limit of detection in all cases but remained high in the LN sanctuary sites. Novel latent cells increased systemically over time but very slowly, taking between 25 and 50 years to reach 5 % of the total latent pool, depending on the volume of lymphoid tissue involvement. Putative sanctuary sites in LNs are limited in volume and produce novel latent cells slowly. Assays to detect genetic drift due to such sites would require very deep sequencing if sampling only from the blood. Previous studies showing a lack of genetic drift are consistent with the expected contribution of ongoing replication in lymph node sanctuary sites.

Topological data analysis of antibody dynamics of severe and non-severe patients with COVID-19

The COVID-19 pandemic is a significant public health threat with unanswered questions regarding the immune system's role in the disease's severity level. Here, based on antibody kinetic data of severe and non-severe COVID-19 patients, topological data analysis (TDA) highlights that severity is not binary. However, there are differences in the shape of antibody responses that further classify COVID-19 patients into non-severe, severe, and intermediate cases of severity. Based on the results of TDA, different mathematical models were developed to represent the dynamics between the different severity groups. The best model was the one with the lowest average value of the Akaike Information Criterion for all groups of patients. Our results suggest that different immune mechanisms drive differences between the severity groups. Further inclusion of different longitudinal data sets will be central for a holistic way of tackling COVID-19.

HIV infection dynamics and viral rebound: Modeling results from humanized mice

Despite years of combined antiretroviral therapy (cART), HIV persists in infected individuals. The virus also rebounds after the cessation of cART. The sources contributing to viral persistence and rebound are not fully understood. When viral rebound occurs, what affects the time to rebound and how to delay the rebound remain unclear. In this paper, we started with the data fitting of an HIV infection model to the viral load data in treated and untreated humanized myeloid-only mice (MoM) in which macrophages serve as the target of HIV infection. By fixing the parameter values for macrophages from the MoM fitting, we fit a mathematical model including the infection of two target cell populations to the viral load data from humanized bone marrow/liver/thymus (BLT) mice, in which both CD4+ T cells and macrophages are the target of HIV infection. Data fitting suggests that the viral load decay in BLT mice under treatment has three phases. The loss of infected CD4+ T cells and macrophages is a major contributor to the first two phases of viral decay, and the last phase may be due to the latent infection of CD4+ T cells. Numerical simulations using parameter estimates from the data fitting show that the pre-ART viral load and the latent reservoir size at treatment cessation can affect viral growth rate and predict the time to viral rebound. Model simulations further reveal that early and prolonged cART can delay the viral rebound after cessation of treatment, which may have implications in the search for functional control of HIV infection.

Ongoing HIV replication in lymph node sanctuary sites in treated patients contributes to the total latent HIV at a very slow rate

Lymph nodes (LNs) serve as a sanctuary site for HIV viruses due to the heterogeneous distribution of the antiretrovirals (ARVs) inside the LNs. There is an ongoing debate whether this represents ongoing cycles of viral replication in the LNs or merely residual virus production by latently infected cells. Previous work has claimed that the measured levels of genetic variation in proviruses sampled from the blood were inconsistent with ongoing replication. However, it is not clear what rate of variation is consistent with ongoing replication in small sanctuary sites. In this study, we used a spherically symmetric compartmental ODE model to track the HIV viral dynamics in the LN and predict the contribution of ongoing replication within the LN to the wholebody proviral pool in an ARV-suppressed patient. This model tracks the reaction-diffusion dynamics of uninfected, actively infected, and latently infected T-cells as well as free virus within the LN parenchyma and the blood, and distinguishes between latently infected cells created before ARV therapy and during ARV therapy. We simulated suppressive therapy beginning in year 5 post-infection. Each LN sanctuary site had a volume of 1 ml, and we considered cases of 1ml, 30ml, and 250ml total volume, which represent a single active sanctuary site, moderate systemic involvement, and involvement of the total lymphoid tissue. Viral load in the blood rapidly dropped and remained below the limit of detection in all cases but remained high in the LN sanctuary sites. Novel latent cells increased systemically over time but very slowly, taking between 25 and 50 years to reach 5% of the total latent pool, depending on the volume of lymphoid tissue involvement. Putative sanctuary sites in LNs are limited in volume and produce novel latent cells slowly. Assays to detect genetic drift due to such sites would require very deep sequencing if sampling only from the blood. Previous studies showing a lack of genetic drift are consistent with the expected contribution of ongoing replication in lymph node sanctuary sites.

Viral dynamics with immune responses: effects of distributed delays and Filippov antiretroviral therapy

In this paper, we propose a general viral infection model to incorporate two infection modes (virus-to-cell mode and cell-to-cell mode), the CTL immune response, and the distributed intracellular delays during the processes of viral infection, viral production, and CTLs recruitment. We investigate the existence, the uniqueness, and the global stability of three equilibria: infection-free equilibrium [Formula: see text], immune-inactivated equilibrium [Formula: see text] and immune-activated equilibrium [Formula: see text], respectively. We prove that the viral dynamics are determined by two threshold parameters: the basic reproduction number for infection [Formula: see text] and the basic reproduction number for immune response [Formula: see text]. We also numerically explore the viral dynamics beyond stability. We use bifurcation diagrams to show that increasing the delay in CTL immune cell recruitment can induce a switch in viral load from a stable constant level to sustained oscillations, and then back to a stable equilibrium. We also compare the contributions of the two infection modes to the total infection level and identify the key parameters that would affect the percentages of virus-to-cell infection and cell-to-cell infection. Finally, we explore how Filippov control can be applied in antiretroviral therapy to reduce the viral loads.

Towards a new combination therapy with vectored immunoprophylaxis for HIV: Modeling "shock and kill" strategy

Latently infected cells are considered as a major barrier to curing Human Immunodeficiency Virus (HIV) infection. Reactivation of latently infected cells followed by killing the actively infected cells may be a potential strategy ("shock and kill") to purge the latent reservoir. Based on vectored immunoprophylaxis (VIP) experiment that can elicit bNAbs, in this paper a mathematical model is formulated to explore the efficacy of "shock and kill" strategy with VIP. We derive the basic reproduction number R₀ of the model and show that R₀ completely determines the dynamics of the model: if R₀<1, the disease-free equilibrium is globally asymptotically stable; if R₀>1, the system is uniformly persistent. Numerical simulations suggest that the "shock and kill" strategy with VIP can effectively control HIV infection while this strategy cannot eradicate the reservoir without VIP although it can alleviate the HIV infection. To model the administration of drugs and vaccine more realistically, pharmacokinetics and pulse vaccination are incorporated into the model of ordinary differential equations. The resultants are described by impulsive differential equations. The thresholds are obtained for the frequency and strength of the vaccination to eliminate the viruses. Furthermore, the most appropriate times are numerically investigated for starting a short-term latency-reversing agents (LRAs) treatment relative to ART considering the toxicity of LRAs. The results show that LRAs treatment at the beginning of ART might be a better option. These results have important implications for the design of HIV cure-related clinical trials.

Analysis of HIV latent infection model with multiple infection stages and different drug classes

Latently infected CD4+ 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.

Lower Incidence of HIV-1 Blips Observed During Integrase Inhibitor-Based Combination Antiretroviral Therapy

BACKGROUND

As the nature of viral blips remains unclear, their occurrence often leads to uncertainty. This study compares blip incidence rates during treatment with different combination antiretroviral therapy anchors.

SETTING

Retrospective cohort study in a tertiary hospital.

METHODS

All antiretroviral regimens between 2010 and 2020 containing 2 nucleos(-t)ide reverse transcriptase inhibitors and 1 anchor in virologically suppressed people living with HIV (PLWH) from our center were evaluated for the occurrence of blips [isolated viral loads (VLs) 50-499 copies/mL between measurements <50 copies/mL]. Factors associated with blips were identified using multivariable generalized estimating equation-based negative binomial models. The relationship between blips and either persistent low-level viremia (consecutive VLs ≥ 50 copies/mL not classified as failure) or virologic failure (consecutive VLs ≥ 200 or 1 VL ≥ 500 copies/mL) was also evaluated.

RESULTS

In total, 308 blips occurred during 3405 treatment courses in 1661 PLWH. Compared with a non-nucleoside reverse transcriptase inhibitor anchor, blip incidence was higher for protease inhibitors (incidence rate ratio 1.37; 95% confidence interval 1.05 to 1.78) and lower for integrase inhibitors (INSTIs) (incidence rate ratio 0.64; 95% confidence interval: 0.43 to 0.96). In addition, blips were associated with higher zenith VL, higher VL test frequency, and shorter time since antiretroviral therapy initiation. PLWH experiencing blips were more likely to demonstrate persistent low-level viremia but not virologic failure. Blips led to extra consultations and measurements.

CONCLUSIONS

INSTI-based regimens display a low number of blips. Although we found no correlation with virologic failure, the occurrence of blips led to an increased clinical burden. Further research is needed to elucidate the implications and underlying mechanisms of these findings.

Stochastic investigation of HIV infection and the emergence of drug resistance

Drug-resistant HIV-1 has caused a growing concern in clinic and public health. Although combination antiretroviral therapy can contribute massively to the suppression of viral loads in patients with HIV-1, it cannot lead to viral eradication. Continuing viral replication during sub-optimal therapy (due to poor adherence or other reasons) may lead to the accumulation of drug resistance mutations, resulting in an increased risk of disease progression. Many studies also suggest that events occurring during the early stage of HIV-1 infection (i.e., the first few hours to days following HIV exposure) may determine whether the infection can be successfully established. However, the numbers of infected cells and viruses during the early stage are extremely low and stochasticity may play a critical role in dictating the fate of infection. In this paper, we use stochastic models to investigate viral infection and the emergence of drug resistance of HIV-1. The stochastic model is formulated by a continuous-time Markov chain (CTMC), which is derived based on an ordinary differential equation model proposed by Kitayimbwa et al. that includes both forward and backward mutations. An analytic estimate of the probability of the clearance of HIV infection of the CTMC model near the infection-free equilibrium is obtained by a multitype branching process approximation. The analytical predictions are validated by numerical simulations. Unlike the deterministic dynamics where the basic reproduction number R₀ serves as a sharp threshold parameter (i.e., the disease dies out if R₀<1 and persists if R₀>1), the stochastic models indicate that there is always a positive probability for HIV infection to be eradicated in patients. In the presence of antiretroviral therapy, our results show that the chance of clearance of the infection tends to increase although drug resistance is likely to emerge.

Optimal Control of an HIV Model with Gene Therapy and Latency Reversing Agents

In this paper, we study the dynamics of HIV under gene therapy and latency reversing agents. While previous works modeled either the use of gene therapy or latency reversing agents, we consider the effects of a combination treatment strategy. For constant treatment controls, we establish global stability of the disease-free equilibrium and endemic equilibrium based on the value of R0. We then consider time-dependent controls and formulate an associated optimal control problem that emphasizes reduction of the latent reservoir. Characterizations for the optimal control profiles are found using Pontryagin’s Maximum Principle. We perform numerical simulations of the optimal control model using the fourth-order Runge–Kutta forward-backward sweep method. We find that a combination treatment of gene therapy with latency reversing agents provides better remission times than gene therapy alone. We conclude with a discussion of our findings and future work.

The impact of viraemia on inflammatory biomarkers and CD4+ cell subpopulations in HIV-infected children in sub-Saharan Africa

OBJECTIVE

To determine the impact of virological control on inflammation and cluster of differentiation 4 depletion among HIV-infected children initiating antiretroviral therapy (ART) in sub-Saharan Africa.

DESIGN

Longitudinal cohort study.

METHODS

In a sub-study of the ARROW trial (ISRCTN24791884), we measured longitudinal HIV viral loads, inflammatory biomarkers (C-reactive protein, tumour necrosis factor alpha, interleukin 6 (IL-6), soluble CD14) and (Uganda only) whole blood immunophenotype by flow cytometry in 311 Zimbabwean and Ugandan children followed for median 3.5 years on first-line ART. We classified each viral load measurement as consistent suppression, blip/post-blip, persistent low-level viral load or rebound. We used multi-level models to estimate rates of increase or decrease in laboratory markers, and Poisson regression to estimate the incidence of clinical events.

RESULTS

Overall, 42% children experienced viral blips, but these had no significant impact on immune reconstitution or inflammation. Persistent detectable viraemia occurred in one-third of children and prevented further immune reconstitution, but had little impact on inflammatory biomarkers. Virological rebound to ≥5000 copies/ml was associated with arrested immune reconstitution, rising IL-6 and increased risk of clinical disease progression.

CONCLUSIONS

As viral load testing becomes more available in sub-Saharan Africa, repeat testing algorithms will be required to identify those with virological rebound, who need switching to prevent disease progression, whilst preventing unnecessary second-line regimen initiation in the majority of children with detectable viraemia who remain at low risk of disease progression.

Controlling of pandemic COVID-19 using optimal control theory

In 2019, a new infectious disease called pandemic COVID-19 began to spread from Wuhan, China. In spite of the efforts to stop the disease, being out of the control of the governments it spread rapidly all over the world. From then on, much research has been done in the world with the aim of controlling this contagious disease. A mathematical model for modeling the spread of COVID-19 and also controlling the spread of the disease has been presented in this paper. We find the disease-free equilibrium points as trivial equilibrium (TE), virus absenteeism equilibrium (VAE) and virus incidence equilibrium (VIE) for the proposed model; and at the trivial equilibrium point for the presented dynamic system we obtain the Jacobian matrix so as to be used in finding the largest eigenvalue. Radius spectral method has been used for finding the reproductive number. In the following, by adding a controller to the model and also using the theory of optimal control, we can improve the performance of the model. We must have a correct understanding of the system i.e. how it works, the various variables affecting the system, and the interaction of the variables on each other. To search for the optimal values, we need to use an appropriate optimization method. Given the limitations and needs of the problem, the aim of the optimization is to find the best solutions, to find conditions that result in the maximum of susceptiblity, the minimum of infection, and optimal quarantination.

Dynamics of a new HIV model with the activation status of infected cells

The activation status can dictate the fate of an HIV-infected CD4+ T cell. Infected cells with a low level of activation remain latent and do not produce virus, while cells with a higher level of activation are more productive and thus likely to transfer more virions to uninfected cells during cell-to-cell transmission. How the activation status of infected cells affects HIV dynamics under antiretroviral therapy remains unclear. We develop a new mathematical model that structures the population of infected cells continuously according to their activation status. The effectiveness of antiretroviral drugs in blocking cell-to-cell viral transmission decreases as the level of activation of infected cells increases because the more virions are transferred from infected to uninfected cells during cell-to-cell transmission, the less effectively the treatment is able to inhibit the transmission. The basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}$$\end{document}R0 of the model is shown to determine the existence and stability of the equilibria. Using the principal spectral theory and comparison principle, we show that the infection-free equilibrium is locally and globally asymptotically stable when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}$$\end{document}R0 is less than one. By constructing Lyapunov functional, we prove that the infected equilibrium is globally asymptotically stable when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}$$\end{document}R0 is greater than one. Numerical investigation shows that even when treatment can completely block cell-free virus infection, virus can still persist due to cell-to-cell transmission. The random switch between infected cells with different activation levels can also contribute to the replenishment of the latent reservoir, which is considered as a major barrier to viral eradication. This study provides a new modeling framework to study the observations, such as the low viral load persistence, extremely slow decay of latently infected cells and transient viral load measurements above the detection limit, in HIV-infected patients during suppressive antiretroviral therapy.

Backward bifurcation in within-host HIV models

The activation and proliferation of naive CD4 T cells produce helper T cells, and increase the susceptible population in the presence of HIV. This may cause backward bifurcation. To verify this, we construct a simple within-host HIV model that includes the key variables, namely healthy naive CD4 T cells, helper T cells, infected CD4 T cells and virus. When the viral basic reproduction number R₀ is less than unity, we show theoretically and numerically that bistability for R_C<R₀<1 can be caused by a backward bifurcation due to a new susceptible population produced by activation of healthy naive CD4 T cells that become helper T cells. An extended model including the CTL dynamics may also show this backward bifurcation. In the case that the homeostatic source of healthy naive CD4 T cells is large, R_C is approximately the threshold for HIV to persist independent of initial conditions. The backward bifurcation may still occur even when we consider latent infections of naive CD4 T cells. Thus to control the spread of within-host HIV, it may be necessary for treatment to reduce the reproduction number below R_C.

Dynamical characterization of antiviral effects in COVID-19

Mathematical models describing SARS-CoV-2 dynamics and the corresponding immune responses in patients with COVID-19 can be critical to evaluate possible clinical outcomes of antiviral treatments. In this work, based on the concept of virus spreadability in the host, antiviral effectiveness thresholds are determined to establish whether or not a treatment will be able to clear the infection. In addition, the virus dynamic in the host - including the time-to-peak and the final monotonically decreasing behavior - is characterized as a function of the time to treatment initiation. Simulation results, based on nine patient data, show the potential clinical benefits of a treatment classification according to patient critical parameters. This study is aimed at paving the way for the different antivirals being developed to tackle SARS-CoV-2.

HTLV/HIV Dual Infection: Modeling and Analysis

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.

Block-And-Lock: New Horizons for a Cure for HIV-1

HIV-1/AIDS remains a global public health problem. The world health organization (WHO) reported at the end of 2019 that 38 million people were living with HIV-1 worldwide, of which only 67% were accessing antiretroviral therapy (ART). Despite great success in the clinical management of HIV-1 infection, ART does not eliminate the virus from the host genome. Instead, HIV-1 remains latent as a viral reservoir in any tissue containing resting memory CD4⁺ T cells. The elimination of these residual proviruses that can reseed full-blown infection upon treatment interruption remains the major barrier towards curing HIV-1. Novel approaches have recently been developed to excise or disrupt the virus from the host cells (e.g., gene editing with the CRISPR-Cas system) to permanently shut off transcription of the virus (block-and-lock and RNA interference strategies), or to reactivate the virus from cell reservoirs so that it can be eliminated by the immune system or cytopathic effects (shock-and-kill strategy). Here, we will review each of these approaches, with the major focus placed on the block-and-lock strategy.

Viral dynamics of a latent HIV infection model with Beddington-DeAngelis incidence function, B-cell immune response and multiple delays

In this paper, an HIV infection model with latent infection, Beddington-DeAngelis infection function, B-cell immune response and four time delays is formulated. The well-posedness of the model solution is rigorously derived, and the basic reproduction number $\mathcal{R}_0$ and the B-cell immune response reproduction number $\mathcal{R}_1$ are also obtained. By analyzing the modulus of the characteristic equation and constructing suitable Lyapunov functions, we establish the global asymptotic stability of the uninfected and the B-cell-inactivated equilibria for the four time delays, respectively. Hopf bifurcation occurs at the B-cell-activated equilibrium when the model includes the immune delay, and the B-cell-activated equilibrium is globally asymptotically stable if the model does not include it. Numerical simulations indicate that the increase of the latency delay, the cell infection delay and the virus maturation delay can cause the B-cell-activated equilibrium stabilize, while the increase of the immune delay can cause it destabilize.

Modeling HIV-1 infection in the brain

While highly active antiretroviral therapy (HAART) is successful in controlling the replication of Human Immunodeficiency Virus (HIV-1) in many patients, currently there is no cure for HIV-1, presumably due to the presence of reservoirs of the virus. One of the least studied viral reservoirs is the brain, which the virus enters by crossing the blood-brain barrier (BBB) via macrophages, which are considered as conduits between the blood and the brain. The presence of HIV-1 in the brain often leads to HIV associated neurocognitive disorders (HAND), such as encephalitis and early-onset dementia. In this study we develop a novel mathematical model that describes HIV-1 infection in the brain and in the plasma coupled via the BBB. The model predictions are consistent with data from macaques infected with a mixture of simian immunodeficiency virus (SIV) and simian-human immunodeficiency virus (SHIV). Using our model, we estimate the rate of virus transport across the BBB as well as viral replication inside the brain, and we compute the basic reproduction number. We also carry out thorough sensitivity analysis to define the robustness of the model predictions on virus dynamics inside the brain. Our model provides useful insight into virus replication within the brain and suggests that the brain can be an important reservoir causing long-term viral persistence.

Mathematical modeling of hepatitis C RNA replication, exosome secretion and virus release

Hepatitis C virus (HCV) causes acute hepatitis C and can lead to life-threatening complications if it becomes chronic. The HCV genome is a single plus strand of RNA. Its intracellular replication is a spatiotemporally coordinated process of RNA translation upon cell infection, RNA synthesis within a replication compartment, and virus particle production. While HCV is mainly transmitted via mature infectious virus particles, it has also been suggested that HCV-infected cells can secrete HCV RNA carrying exosomes that can infect cells in a receptor independent manner. In order to gain insight into these two routes of transmission, we developed a series of intracellular HCV replication models that include HCV RNA secretion and/or virus assembly and release. Fitting our models to in vitro data, in which cells were infected with HCV, suggests that initially most secreted HCV RNA derives from intracellular cytosolic plus-strand RNA, but subsequently secreted HCV RNA derives equally from the cytoplasm and the replication compartments. Furthermore, our model fits to the data suggest that the rate of virus assembly and release is limited by host cell resources. Including the effects of direct acting antivirals in our models, we found that in spite of decreasing intracellular HCV RNA and extracellular virus concentration, low level HCV RNA secretion may continue as long as intracellular RNA is available. This may possibly explain the presence of detectable levels of plasma HCV RNA at the end of treatment even in patients that ultimately attain a sustained virologic response.

Approximately 70 million people are chronically infected with hepatitis C virus (HCV), which if left untreated may lead to cirrhosis and liver cancer. However, modern drug therapy is highly effective and hepatitis C is the first chronic virus infection that can be cured with short-term therapy in almost all infected individuals. The within-host transmission of HCV occurs mainly via infectious virus particles, but experimental studies suggest that there may be additional receptor-independent cell-to-cell transmission by exosomes that carry the HCV genome. In order to understand the intracellular HCV lifecycle and HCV RNA spread, we developed a series of mathematical models that take both exosomal secretion and viral secretion into account. By fitting these models to in vitro data, we found that secretion of both HCV RNA as well as virus probably occurs and that the rate of virus assembly is likely limited by cellular co-factors on which the virus strongly depends for its own replication. Furthermore, our modeling predicted that the parameters governing the processes in the viral lifecycle that are targeted by direct acting antivirals are the most sensitive to perturbations, which may help explain their ability to cure this infection.

Use of human peripheral blood mononuclear cells to define immunological properties of nucleic acid nanoparticles

This protocol assesses proinflammatory properties of nucleic acid nanoparticles (NANPs) using a validated preclinical model, peripheral blood mononuclear cells (PBMCs), that is highly predictive of cytokine responses. The experimental procedure details the preparation of pyrogen-free NANPs, isolation of PBMCs from freshly collected human blood, and analysis of characteristic biomarkers (type I and III interferons) produced by PBMCs transfected with NANPs. Although representative NANPs with high and low immunostimulatory potential are used as standards throughout the procedure, this protocol can be adapted to any NANPs or therapeutic nucleic acids, irrespective of whether they are carrier based or carrier free; additional cytokine biomarkers can also be included. We test several commercial platforms and controls broadly accessible to the research community to quantify all biomarkers in either single- or multiplex format. The continuous execution of this protocol takes <48 h; when immediate analysis is not feasible, single-use aliquots of the supernatants can be frozen and stored (-20 °C; 12 months).

In-host Mathematical Modelling of COVID-19 in Humans

COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat to human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. Considering different starting times of infection, mathematical models are proposed to represent SARS-CoV-2 dynamics in infected patients. Based on the target cell limited model, the within-host reproductive number for SARS-CoV-2 is consistent with the broad values of human influenza infection. The best model to fit the data was including immune cell response, which suggests a slow immune response peaking between 5 to 10 days post-onset of symptoms. The model with the eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. Interestingly, model simulations predict that SARS-CoV-2 may replicate very slowly in the first days after infection, and viral load could be below detection levels during the first 4 days post infection. A quantitative comprehension of SARS-CoV-2 dynamics and the estimation of standard parameters of viral infections is the key contribution of this pioneering work. These models can serve for future evaluation of control theoretical approaches to tailor new drugs against COVID-19.

Modeling HIV multiple infection

Multiple infection of target cells by human immunodeficiency virus (HIV) may lead to viral escape from host immune responses and drug resistance to antiretroviral therapy, bringing more challenges to the control of infection. The mechanisms underlying HIV multiple infection and their relative contributions are not fully understood. In this paper, we develop and analyze a mathematical model that includes sequential cell-free virus infection (i.e.one virus is transmitted each time in a sequential infection of target cells by virus) and cell-to-cell transmission (i.e.multiple viral genomes are transmitted simultaneously from infected to uninfected cells). By comparing model prediction with the distribution data of proviral genomes in HIV-infected spleen cells, we find that multiple infection can be well explained when the two modes of viral transmission are both included. Numerical simulation using the parameter estimates from data fitting shows that the majority of T cell infections are attributed to cell-to-cell transmission and this transmission mode also accounts for more than half of cell's multiple infections. These results suggest that cell-to-cell transmission plays a critical role in forming HIV multiple infection and thus has important implications for HIV evolution and pathogenesis.

Impact of low-level viraemia on virological failure among Asian children with perinatally acquired HIV on first-line combination antiretroviral treatment: a multicentre, retrospective cohort study

INTRODUCTION

The clinical relevance of low-level viraemia (LLV) and virological outcomes among children living with HIV (CLHIV) remains controversial. This study aimed to determine the impact of LLV on virological failure (VF) among Asian CLHIV on first-line combination antiretroviral therapy (cART).

METHODS

CLHIV aged <18 years, who were on first-line cART for ≥12 months, and had virological suppression (two consecutive plasma viral load [pVL] <50 copies/mL) were included. Those who started treatment with mono/dual antiretroviral therapy, had a history of treatment interruption >14 days, or received treatment and care at sites with a pVL lower limit of detection >50 copies/mL were excluded. LLV was defined as a pVL 50 to 1000 copies/mL, and VF as a single pVL >1000 copies/mL. Baseline was the time of the second pVL < 50 copies/mL. Cox proportional hazards models were performed to assess the association between LLV and VF.

RESULTS

From January 2008 to September 2016, 508 CLHIV (55% female) were eligible for the study. At baseline, the median age was 9.6 (IQR: 7.0 to 12.3) years, cART duration was 1.4 (IQR: 1.3 to 1.8) years, 97% of CLHIV were on non-nucleoside reverse transcriptase inhibitor-based regimens, and the median CD4 was 25% (IQR: 20% to 30%). Over a median follow-up time of 6.0 (IQR: 3.1 to 8.9) years from baseline, 86 CLHIV (17%) had ever experienced LLV, of whom 32 (37%) had multiple LLV episodes. Female sex, living in Malaysia (compared to Cambodia), having family members other than biological parents/grandparents as a primary caregiver, and baseline CD4 < 25% increased risk of LLV. Overall, 115 children (23%) developed VF, corresponding to a rate of 4.0 (95%CI: 3.4 to 4.9) per 100 person-years of follow-up (PYFU). VF was greater among children who had ever experienced LLV compared with those who maintained virological suppression throughout the study period (8.9 vs. 3.3 per 100 PYFU; p < 0.001). In multivariable analyses, ever experiencing LLV was associated with increased risk of subsequent VF (adjusted hazard ratio: 3.01; 95%CI: 1.97 to 4.60).

CONCLUSIONS

LLV increased the risk of subsequent VF among Asian CLHIV who had previously been suppressed on first-line cART. Adherence interventions and additional targeted pVL monitoring may be warranted among children with LLV to facilitate early detection of VF.

Modeling the role of macrophages in HIV persistence during antiretroviral therapy

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.

A Coupled Mathematical Model of the Intracellular Replication of Dengue Virus and the Host Cell Immune Response to Infection

Dengue virus (DV) is a positive-strand RNA virus of the Flavivirus genus. It is one of the most prevalent mosquito-borne viruses, infecting globally 390 million individuals per year. The clinical spectrum of DV infection ranges from an asymptomatic course to severe complications such as dengue hemorrhagic fever (DHF) and dengue shock syndrome (DSS), the latter because of severe plasma leakage. Given that the outcome of infection is likely determined by the kinetics of viral replication and the antiviral host cell immune response (HIR) it is of importance to understand the interaction between these two parameters. In this study, we use mathematical modeling to characterize and understand the complex interplay between intracellular DV replication and the host cells' defense mechanisms. We first measured viral RNA, viral protein, and virus particle production in Huh7 cells, which exhibit a notoriously weak intrinsic antiviral response. Based on these measurements, we developed a detailed intracellular DV replication model. We then measured replication in IFN competent A549 cells and used this data to couple the replication model with a model describing IFN activation and production of IFN stimulated genes (ISGs), as well as their interplay with DV replication. By comparing the cell line specific DV replication, we found that host factors involved in replication complex formation and virus particle production are crucial for replication efficiency. Regarding possible modes of action of the HIR, our model fits suggest that the HIR mainly affects DV RNA translation initiation, cytosolic DV RNA degradation, and naïve cell infection. We further analyzed the potential of direct acting antiviral drugs targeting different processes of the DV lifecycle in silico and found that targeting RNA synthesis and virus assembly and release are the most promising anti-DV drug targets.

Andronov-Hopf and Neimark-Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations

In many areas, researchers might think that a differential equation model is required, but one might be forced to use an approximate difference equation model if data is only available at discrete points in time. In this paper, a detailed comparison is given of the behavior of continuous and discrete models for two representative time-delay models, namely a model for HIV and an extended logistic growth model. For each model, there are seven different time-delay versions because there are seven different positions to include time delays. For the seven different time-delay versions of each model, proofs are given of necessary and sufficient conditions for the existence and stability of equilibrium points and for the existence of Andronov-Hopf bifurcations in the differential equations and Neimark-Sacker bifurcations in the difference equations. We show that only five of the seven time-delay versions have bifurcations and that all bifurcation versions have supercritical limit cycles with one having a repelling cycle and four having attracting cycles. Numerical simulations are used to illustrate the analytical results and to show that critical times for Neimark-Sacker bifurcations are less than critical times for Andronov-Hopf bifurcations but converge to them as the time step of the discretization tends to zero.

Mycobacterium tuberculosis Reactivates HIV-1 via Exosome-Mediated Resetting of Cellular Redox Potential and Bioenergetics

The synergy between Mycobacterium tuberculosis and human immunodeficiency virus-1 (HIV-1) interferes with therapy and facilitates the pathogenesis of both human pathogens. Fundamental mechanisms by which M. tuberculosis exacerbates HIV-1 infection are not clear. Here, we show that exosomes secreted by macrophages infected with M. tuberculosis, including drug-resistant clinical strains, reactivated HIV-1 by inducing oxidative stress. Mechanistically, M. tuberculosis-specific exosomes realigned mitochondrial and nonmitochondrial oxygen consumption rates (OCR) and modulated the expression of host genes mediating oxidative stress response, inflammation, and HIV-1 transactivation. Proteomics analyses revealed the enrichment of several host factors (e.g., HIF-1α, galectins, and Hsp90) known to promote HIV-1 reactivation in M. tuberculosis-specific exosomes. Treatment with a known antioxidant-N-acetyl cysteine (NAC)-or with inhibitors of host factors-galectins and Hsp90-attenuated HIV-1 reactivation by M. tuberculosis -specific exosomes. Our findings uncover new paradigms for understanding the redox and bioenergetics bases of HIV-M. tuberculosis coinfection, which will enable the design of effective therapeutic strategies.IMPORTANCE Globally, individuals coinfected with the AIDS virus (HIV-1) and with M. tuberculosis (causative agent of tuberculosis [TB]) pose major obstacles in the clinical management of both diseases. At the heart of this issue is the apparent synergy between the two human pathogens. On the one hand, mechanisms induced by HIV-1 for reactivation of TB in AIDS patients are well characterized. On the other hand, while clinical findings clearly identified TB as a risk factor for HIV-1 reactivation and associated mortality, basic mechanisms by which M. tuberculosis exacerbates HIV-1 replication and infection remain poorly characterized. The significance of our research is in identifying the role of fundamental mechanisms such as redox and energy metabolism in catalyzing HIV-M. tuberculosis synergy. The quantification of redox and respiratory parameters affected by M. tuberculosis in stimulating HIV-1 will greatly enhance our understanding of HIV-M. tuberculosis coinfection, leading to a wider impact on the biomedical research community and creating new translational opportunities.

Nucleic Acid Nanoparticles at a Crossroads of Vaccines and Immunotherapies

Vaccines and immunotherapies involve a variety of technologies and act through different mechanisms to achieve a common goal, which is to optimize the immune response against an antigen. The antigen could be a molecule expressed on a pathogen (e.g., a disease-causing bacterium, a virus or another microorganism), abnormal or damaged host cells (e.g., cancer cells), environmental agent (e.g., nicotine from a tobacco smoke), or an allergen (e.g., pollen or food protein). Immunogenic vaccines and therapies optimize the immune response to improve the eradication of the pathogen or damaged cells. In contrast, tolerogenic vaccines and therapies retrain or blunt the immune response to antigens, which are recognized by the immune system as harmful to the host. To optimize the immune response to either improve the immunogenicity or induce tolerance, researchers employ different routes of administration, antigen-delivery systems, and adjuvants. Nanocarriers and adjuvants are of particular interest to the fields of vaccines and immunotherapy as they allow for targeted delivery of the antigens and direct the immune response against these antigens in desirable direction (i.e., to either enhance immunogenicity or induce tolerance). Recently, nanoparticles gained particular attention as antigen carriers and adjuvants. This review focuses on a particular subclass of nanoparticles, which are made of nucleic acids, so-called nucleic acid nanoparticles or NANPs. Immunological properties of these novel materials and considerations for their clinical translation are discussed.

Functional cure of HIV: the scale of the challenge

A variety of interventions to induce a functional cure of HIV are being explored, with the aim being to allow patients to cease antiretroviral therapy (ART) for prolonged periods of time or for life. These interventions share the goal of inducing ART-free remission from HIV pathogenesis and disease progression but achieve this in quite different ways, by reducing the size of the latent reservoir (for example, small-molecule stimulation of latently infected cells), reducing the number of target cells available for the virus (for example, gene therapy) or improving immune responses (for example, active or passive immunotherapy). Here, we consider a number of these alternative strategies for inducing post-treatment control of HIV and use mathematical modelling to predict the scale of the challenge inherent in these different approaches. For many approaches, over 99.9% efficacy will likely be required to induce durable ART-free remissions. The efficacy of individual approaches is currently far below what we predict will be necessary, and new technologies to achieve lifelong functional cure are needed.

Modelling epidemics with fractional-dose vaccination in response to limited vaccine supply

The control strategies of emergency infectious diseases are constrained by limited medical resources. The fractional dose vaccination strategy as one of feasible strategies was proposed in response to global shortages of vaccine stockpiles. Although a variety of epidemic models have been developed under the circumstances of limited resources in treatment, few models particularly investigated vaccination strategies in resource-limited settings. In this paper, we develop a two-group SIR model with incorporation of proportionate mixing patterns and n-fold fractional dose vaccination related parameters to evaluate the efficiency of fractional dose vaccination on disease control at the population level. The existence and uniqueness of the final size of the two-group SIR epidemic model, the formulation of the basic reproduction number and the relationship between them are established. Moreover, numerical simulations are performed based on this two-group vector-free model to investigate the effectiveness of n-fold fractional dose vaccination by using the emergency outbreaks of yellow fever in Angola in 2016. By employing linear and nonlinear dose-response relationships, we compare the resulting fluctuations of four characteristics of the epidemics, which are the outbreak size, the peak time of the outbreak, the basic reproduction number and the infection attack rate (IAR). For both types of dose-response relationships, dose-fractionation takes positive effects in lowering the outbreak size, delay the peak time of the outbreak, reducing the basic reproduction number and the IAR of yellow fever only when the vaccine efficacy is high enough. Moreover, five-fold fractional dose vaccination strategy may not be the optimal vaccination strategy as proposed by the World Health Organization if the dose-response relationship is nonlinear.

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

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.

Predictions of time to HIV viral rebound following ART suspension that incorporate personal biomarkers

Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. Suspension of therapy is followed by rebound of viral loads to high, pre-therapy levels. However, there is significant heterogeneity in speed of rebound, with some rebounds occurring within days, weeks, or sometimes years. We present a stochastic mathematical model to gain insight into these post-treatment dynamics, specifically characterizing the dynamics of short term viral rebounds (≤ 60 days). Li et al. (2016) report that the size of the expressed HIV reservoir, i.e., cell-associated HIV RNA levels, and drug regimen correlate with the time between ART suspension and viral rebound to detectable levels. We incorporate this information and viral rebound times to parametrize our model. We then investigate insights offered by our model into the underlying dynamics of the latent reservoir. In particular, we refine previous estimates of viral recrudescence after ART interruption by accounting for heterogeneity in infection rebound dynamics, and determine a recrudescence rate of once every 2-4 days. Our parametrized model can be used to aid in design of clinical trials to study viral dynamics following analytic treatment interruption. We show how to derive informative personalized testing frequencies from our model and offer a proof-of-concept example. Our results represent first steps towards a model that can make predictions on a person living with HIV (PLWH)'s rebound time distribution based on biomarkers, and help identify PLWH with long viral rebound delays.

Virus dynamics and phyloanatomy: Merging population dynamic and phylogenetic approaches

In evolutionary biology and epidemiology, phylodynamic methods are widely used to infer population biological characteristics, such as the rates of replication, death, migration, or, in the epidemiological context, pathogen spread. More recently, these methods have been used to elucidate the dynamics of viruses within their hosts. Especially the application of phylogeographic approaches has the potential to shed light on anatomical colonization pathways and the exchange of viruses between distinct anatomical compartments. We and others have termed this phyloanatomy. Here, we review the promise and challenges of phyloanatomy, and compare them to more classical virus dynamics and population genetic approaches. We argue that the extremely strong selection pressures that exist within the host may represent the main obstacle to reliable phyloanatomic analysis.

Efficacy of the Post-Exposure Prophylaxis and of the HIV Latent Reservoir in HIV Infection

We propose a fractional order model to study the efficacy of the Post-Exposure Prophylaxis (PEP) in human immunodeficiency virus (HIV) within-host dynamics, in the presence of the HIV latent reservoir. Latent reservoirs harbor infected cells that contain a transcriptionally silent but reactivatable provirus. The latter constitutes a major difficulty to the eradication of HIV in infected patients. PEP is used as a way to prevent HIV infection after a recent possible exposure to HIV. It consists of the in-take of antiretroviral drugs for, usually, 28 days. In this study, we focus on the dosage and dosage intervals of antiretroviral therapy (ART) during PEP and in the role of the latent reservoir in HIV infected patients. We thus simulate the model for immunologically important parameters concerning the drugs and the fraction of latently infected cells. The results may add important information to clinical practice of HIV infected patients.

Modeling HIV Dynamics Under Combination Therapy with Inducers and Antibodies

A mathematical model is proposed to simulate the "shock-kill" strategy where broadly neutralizing antibodies (bNAbs) are injected with a combination of HIV latency activators to reduce persistent HIV reservoirs. The basic reproductive ratio of virus is computed to extrapolate how the combinational therapy of inducers and antibodies affects the persistence of HIV infection. Numerical simulations demonstrate that a proper combination of inducers and bNAbs can drive the basic reproductive ratio below unity. Interestingly, it is found that a longer dosage interval leads to the higher HIV survival opportunity and a smaller dosage interval is preferred, which is fundamental to design an optimal therapeutic scheme. Further simulations reveal the conditions under which the joint therapy of inducer and antibodies induces a large extension of viral rebound time, which highlights the mechanism of delayed viral rebound from the experiment (Halper-Stromberg et al. in Cell 158:989-999, 2014). Optimal time for cessation of treatment is also analyzed to aid practical applications.

The Tat inhibitor didehydro-cortistatin A suppresses SIV replication and reactivation

The HIV-1 transactivation protein (Tat) binds the HIV mRNA transactivation responsive element (TAR), regulating transcription and reactivation from latency. Drugs against Tat are unfortunately not clinically available. We reported that didehydro-cortistatin A (dCA) inhibits HIV-1 Tat activity. In human CD4⁺ T cells isolated from aviremic individuals and in the humanized mouse model of latency, combining dCA with antiretroviral therapy accelerates HIV-1 suppression and delays viral rebound upon treatment interruption. This drug class is amenable to block-and-lock functional cure approaches, aimed at a durable state of latency. Simian immunodeficiency virus (SIV) infection of rhesus macaques (RhMs) is the best-characterized model for AIDS research. Here, we demonstrate, using in vitro and cell-based assays, that dCA directly binds to SIV Tat's basic domain. dCA specifically inhibits SIV Tat binding to TAR, but not a Tat-Rev fusion protein, which activates transcription when Rev binds to its cognate RNA binding site replacing the apical region of TAR. Tat-TAR inhibition results in loss of RNA polymerase II recruitment to the SIV promoter. Importantly, dCA potently inhibits SIV reactivation from latently infected Hut78 cells and from primary CD4⁺ T cells explanted from SIV_mac239-infected RhMs. In sum, dCA's remarkable breadth of activity encourages SIV-infected RhM use for dCA preclinical evaluation.-Mediouni, S., Kessing, C. F., Jablonski, J. A., Thenin-Houssier, S., Clementz, M., Kovach, M. D., Mousseau, G., de Vera, I.M.S., Li, C., Kojetin, D. J., Evans, D. T., Valente, S. T. The Tat inhibitor didehydro-cortistatin A suppresses SIV replication and reactivation.

Stochastic Modeling and Simulation of Viral Evolution

RNA viruses comprise vast populations of closely related, but highly genetically diverse, entities known as quasispecies. Understanding the mechanisms by which this extreme diversity is generated and maintained is fundamental when approaching viral persistence and pathobiology in infected hosts. In this paper, we access quasispecies theory through a mathematical model based on the theory of multitype branching processes, to better understand the roles of mechanisms resulting in viral diversity, persistence and extinction. We accomplish this understanding by a combination of computational simulations and the theoretical analysis of the model. In order to perform the simulations, we have implemented the mathematical model into a computational platform capable of running simulations and presenting the results in a graphical format in real time. Among other things, we show that the establishment of virus populations may display four distinct regimes from its introduction into new hosts until achieving equilibrium or undergoing extinction. Also, we were able to simulate different fitness distributions representing distinct environments within a host which could either be favorable or hostile to the viral success. We addressed the most used mechanisms for explaining the extinction of RNA virus populations called lethal mutagenesis and mutational meltdown. We were able to demonstrate a correspondence between these two mechanisms implying the existence of a unifying principle leading to the extinction of RNA viruses.

Increased inflammation in sanctuary sites may explain viral blips in HIV infection

Combined antiretroviral therapy (cART) suppress HIV-1 viral replication, such that viral load in plasma remains below the limit of detection in standard assays. However, intermittent episodes of transient viremia (blips) occur in a set of HIV-patients. Given that follicular hyperplasia occurs during lymphoid inflammation as a normal response to infection, it is hypothesised that when the diameter of the lymph node follicle (LNF) increases and crosses a critical size, a viral blip occurs due to cryptic viremia. To study this hypothesis, a theoretical analysis of a mathematical model is performed to find the conditions for virus suppression in all compartments and different scenarios of LNF size changes are simulated. According to the analysis, blips with duration of around 30 days arise when the diameter rise rate is between 0.02 and 0.03 days(-1). Moreover, the final diameter of the site is directly related to the steady states of the virus load after the occurrence of a blip. When the value of R0 is around 2.1, to have a steady-state below the limit of detection after the viral blip, the maximum final diameters should be greater than 0.7 mm so that there is a relative loss of connection between compartments.

EFFECTS OF ECLIPSE PHASE AND DELAY ON THE DYNAMICS OF HIV INFECTION

In this paper, an HIV infection model with eclipse phase, humoral immune response and immunological delay has been discussed. By studying the characteristic equations of the model, the local stability analysis of various equilibrium points has been explored. Treating the delay as the bifurcation parameter, it has been shown that the delay can destabilize the stability of the infected steady-state leading to Hopf bifurcation and periodic solutions. By using Lyapunov functionals and LaSalle’s invariance principle, the global stability analysis of the boundary equilibrium points has also been explored. It has also been shown numerically that the inclusion of the drug therapy in the model generates sporadic outbursts of virus called viral blips. In the end, numerical simulations have been employed to justify the analytical results proved in the paper. Biologically, the proposed model can explain the presence of viral blips in the system, during the introduction of HAART, as observed in the HIV-infected patient. These blips could mark the viral advancement in the system, thus resulting in complete immunological failure. One of the reasons for these viral blips can be the presence of delay in the activation of immunological response. But the development of drug-resistive virus could also be the reason for this sudden rise in viral loads. Moreover, the incorporation of the delay in the model generates oscillations and periodicity in the model, thus validating the long latency period seen in most HIV-infected patients. Also, a longer delay in the activation of immune response marks a viral advancement in the viral timeline resulting in viral blips, which signify the evolution of the virus.

Global dynamics of a delay virus model with recruitment and saturation effects of immune responses

In this paper, we formulate a virus dynamics model with the recruitment of immune responses, saturation effects and an intracellular time delay. With the help of uniform persistence theory and Lyapunov method, we show that the global stability of the model is totally determined by the basic reproductive number R0. Furthermore, we analyze the effects of the recruitment of immune responses on virus infection by numerical simulation. The results show ignoring the recruitment of immune responses will result in overestimation of the basic reproductive number and the severity of viral infection.

Mathematical Analysis of Viral Replication Dynamics and Antiviral Treatment Strategies: From Basic Models to Age-Based Multi-Scale Modeling

Viral infectious diseases are a global health concern, as is evident by recent outbreaks of the middle east respiratory syndrome, Ebola virus disease, and re-emerging zika, dengue, and chikungunya fevers. Viral epidemics are a socio-economic burden that causes short- and long-term costs for disease diagnosis and treatment as well as a loss in productivity by absenteeism. These outbreaks and their socio-economic costs underline the necessity for a precise analysis of virus-host interactions, which would help to understand disease mechanisms and to develop therapeutic interventions. The combination of quantitative measurements and dynamic mathematical modeling has increased our understanding of the within-host infection dynamics and has led to important insights into viral pathogenesis, transmission, and disease progression. Furthermore, virus-host models helped to identify drug targets, to predict the treatment duration to achieve cure, and to reduce treatment costs. In this article, we review important achievements made by mathematical modeling of viral kinetics on the extracellular, intracellular, and multi-scale level for Human Immunodeficiency Virus, Hepatitis C Virus, Influenza A Virus, Ebola Virus, Dengue Virus, and Zika Virus. Herein, we focus on basic mathematical models on the population scale (so-called target cell-limited models), detailed models regarding the most important steps in the viral life cycle, and the combination of both. For this purpose, we review how mathematical modeling of viral dynamics helped to understand the virus-host interactions and disease progression or clearance. Additionally, we review different types and effects of therapeutic strategies and how mathematical modeling has been used to predict new treatment regimens.

In Vivo Suppression of HIV Rebound by Didehydro-Cortistatin A, a "Block-and-Lock" Strategy for HIV-1 Treatment

HIV-1 Tat activates viral transcription and limited Tat transactivation correlates with latency establishment. We postulated a "block-and-lock" functional cure approach based on properties of the Tat inhibitor didehydro-Cortistatin A (dCA). HIV-1 transcriptional inhibitors could block ongoing viremia during antiretroviral therapy (ART), locking the HIV promoter in persistent latency. We investigated this hypothesis in human CD4⁺ T cells isolated from aviremic individuals. Combining dCA with ART accelerates HIV-1 suppression and prevents viral rebound after treatment interruption, even during strong cellular activation. We show that dCA mediates epigenetic silencing by increasing nucleosomal occupancy at Nucleosome-1, restricting RNAPII recruitment to the HIV-1 promoter. The efficacy of dCA was studied in the bone marrow-liver-thymus (BLT) mouse model of HIV latency and persistence. Adding dCA to ART-suppressed mice systemically reduces viral mRNA in tissues. Moreover, dCA significantly delays and reduces viral rebound levels upon treatment interruption. Altogether, this work demonstrates the potential of block-and-lock cure strategies.