On the intra-host dynamics of HIV-1 infections

Evolutionary safety of lethal mutagenesis driven by antiviral treatment

Nucleoside analogs are a major class of antiviral drugs. Some act by increasing the viral mutation rate causing lethal mutagenesis of the virus. Their mutagenic capacity, however, may lead to an evolutionary safety concern. We define evolutionary safety as a probabilistic assurance that the treatment will not generate an increased number of mutants. We develop a mathematical framework to estimate the total mutant load produced with and without mutagenic treatment. We predict rates of appearance of such virus mutants as a function of the timing of treatment and the immune competence of patients, employing realistic assumptions about the vulnerability of the viral genome and its potential to generate viable mutants. We focus on the case study of Molnupiravir, which is an FDA-approved treatment against Coronavirus Disease-2019 (COVID-19). We estimate that Molnupiravir is narrowly evolutionarily safe, subject to the current estimate of parameters. Evolutionary safety can be improved by restricting treatment with this drug to individuals with a low immunological clearance rate and, in future, by designing treatments that lead to a greater increase in mutation rate. We report a simple mathematical rule to determine the fold increase in mutation rate required to obtain evolutionary safety that is also applicable to other pathogen-treatment combinations.

A novel mathematical model of AIDS-associated Kaposi's sarcoma: Analysis and optimal control

Kaposi's sarcoma (KS) has been the most common HHV-8 virus-induced neoplasm associated with HIV-1 infection. Although the standard KS therapy has not changed in 20 years, not all cases of KS will respond to the same therapy. The goal of current AIDS-KS treatment modalities is to reconstitute the immune system and suppress HIV-1 replication, but newer treatment modalities are on horizon. There are very few mathematical models that have included HIV-1 viral load (VL) measures, despite VL being a key determinant of treatment outcome. Here we introduce a mathematical model that consolidates the effect of both HIV-1 and HHV-8 VL on KS tumor progression by incorporating low or high VLs into the proliferation terms of the immune cell populations. Regulation of HIV-1/HHV-8 VL and viral reservoir cells is crucial for restoring a patient to an asymptomatic stage. Therefore, an optimal control strategy given by a combined antiretroviral therapy (cART) is derived. The results indicate that the drug treatment strategies are capable of removing the viral reservoirs faster and consequently, the HIV-1 and KS tumor burden is reduced. The predictions of the mathematical model have the potential to offer more effective therapeutic interventions based on viral and virus-infected cell load and support new studies addressing the superiority of VL over CD4⁺ T-cell count in HIV-1 pathogenesis.

The Role of Immune Response in Optimal HIV Treatment Interventions

A mathematical model for the transmission dynamics of human immunodeficiency virus (HIV) within a host is developed. Our model focuses on the roles of immune response cells or cytotoxic lymphocytes (CTLs). The model includes active and inactive cytotoxic immune cells. The basic reproduction number and the global stability of the virus free equilibrium is carried out. The model is modified to include anti-retroviral treatment interventions and the controlled reproduction number is explored. Their effects on the HIV infection dynamics are investigated. Two different disease stage scenarios are assessed: early-stage and advanced-stage of the disease. Furthermore, optimal control theory is employed to enhance healthy CD4+ T cells, active cytotoxic immune cells and minimize the total cost of anti-retroviral treatment interventions. Two different anti-retroviral treatment interventions (RTI and PI) are incorporated. The results highlight the key roles of cytotoxic immune response in the HIV infection dynamics and corresponding optimal treatment strategies. It turns out that the combined control (both RTI and PI) and stronger immune response is the best intervention to maximize healthy CD4+ T cells at a minimal cost of treatments.

Effects of neutralizing antibodies on escape from CD8+ T-cell responses in HIV-1 infection

Despite substantial advances in our knowledge of immune responses against HIV-1 and of its evolution within the host, it remains unclear why control of the virus eventually breaks down. Here, we present a new theoretical framework for the infection dynamics of HIV-1 that combines antibody and CD8⁺ T-cell responses, notably taking into account their different lifespans. Several apparent paradoxes in HIV pathogenesis and genetics of host susceptibility can be reconciled within this framework by assigning a crucial role to antibody responses in the control of viraemia. We argue that, although escape from or progressive loss of quality of CD8⁺ T-cell responses can accelerate disease progression, the underlying cause of the breakdown of virus control is the loss of antibody induction due to depletion of CD4⁺ T cells. Furthermore, strong antibody responses can prevent CD8⁺ T-cell escape from occurring for an extended period, even in the presence of highly efficacious CD8⁺ T-cell responses.

Role of active and inactive cytotoxic immune response in human immunodeficiency virus dynamics

Objectives

Mathematical models can be helpful to understand the complex dynamics of human immunodeficiency virus infection within a host. Most of work has studied the interactions of host responses and virus in the presence of active cytotoxic immune cells, which decay to zero when there is no virus. However, recent research highlights that cytotoxic immune cells can be inactive but never be depleted.

Methods

We propose a mathematical model to investigate the human immunodeficiency virus dynamics in the presence of both active and inactive cytotoxic immune cells within a host. We explore the impact of the immune responses on the dynamics of human immunodeficiency virus infection under different disease stages.

Results

Standard mathematical and numerical analyses are presented for this new model. Specifically, the basic reproduction number is computed and local and global stability analyses are discussed.

Conclusion

Our results can give helpful insights when designing more effective drug schedules in the presence of active and inactive immune responses.

Mathematical models of HIV replication and pathogenesis

This review outlines how mathematical models have been helpful, and continue to be so, for obtaining insights into the in vivo dynamics of HIV infection. The review starts with a discussion of a basic mathematical model that has been frequently used to study HIV dynamics. Some crucial results are described, including the estimation of key parameters that characterize the infection, and the generation of influential theories which argued that in vivo virus evolution is a key player in HIV pathogenesis. Subsequently, more recent concepts are reviewed that have relevance for disease progression, including the multiple infection of cells and the direct cell-to-cell transmission of the virus through the formation of virological synapses. These are important mechanisms that can influence the rate at which HIV spreads through its target cell population, which is tightly linked to the rate at which the disease progresses towards AIDS.

Effects of replicative fitness on competing HIV strains

We develop an n-strain model to show the effects of replicative fitness of competing viral strains exerting selective density-dependant infective pressure on each other. A two strain model is used to illustrate the results. A perturbation technique and numerical simulations were used to establish the existence and stability of steady states. More than one infected steady states governed by the replicative fitness resulted from the model exhibiting either strain replacement or co-infection. We found that the presence of two or more HIV strains could result in a disease-free state that, in general, is not globally stable.

Modelling the course of an HIV infection: insights from ecology and evolution

The Human Immunodeficiency Virus (HIV) is one of the most threatening viral agents. This virus infects approximately 33 million people, many of whom are unaware of their status because, except for flu-like symptoms right at the beginning of the infection during the acute phase, the disease progresses more or less symptom-free for 5 to 10 years. During this asymptomatic phase, the virus slowly destroys the immune system until the onset of AIDS when opportunistic infections like pneumonia or Kaposi’s sarcoma can overcome immune defenses. Mathematical models have played a decisive role in estimating important parameters (e.g., virion clearance rate or life-span of infected cells). However, most models only account for the acute and asymptomatic latency phase and cannot explain the progression to AIDS. Models that account for the whole course of the infection rely on different hypotheses to explain the progression to AIDS. The aim of this study is to review these models, present their technical approaches and discuss the robustness of their biological hypotheses. Among the few models capturing all three phases of an HIV infection, we can distinguish between those that mainly rely on population dynamics and those that involve virus evolution. Overall, the modeling quest to capture the dynamics of an HIV infection has improved our understanding of the progression to AIDS but, more generally, it has also led to the insight that population dynamics and evolutionary processes can be necessary to explain the course of an infection.

Effectiveness of a 'hunter' virus in controlling human immunodeficiency virus type 1 infection

Engineered therapeutic viruses provide an alternative method for treating infectious diseases, and mathematical models can clarify the system's dynamics underlying this type of therapy. In particular, this study developed models to evaluate the potential to contain human immunodeficiency virus type 1 (HIV-1) infection using a genetically engineered 'hunter' virus that kills HIV-1-infected cells. First, we constructed a novel model for understanding the progression of HIV infection that predicted the loss of the immune system's CD4(+) T cells across time. Subsequently, it determined the effects of introducing hunter viruses in restoring cell population. The model implemented direct and indirect mechanisms by which HIV-1 may cause cell depletion and an immune response. Results suggest that the slow progression of HIV infection may result from a slowly decaying CTL immune response, leading to a limited but constant removal of uninfected CD4 resting cells through apoptosis - and from resting cell proliferation that reduces the rate of cell depletion over time. Importantly, results show that the hunter virus does restrain HIV infection and has the potential to allow major cell recovery to 'functional' levels. Further, the hunter virus persisted at a reduced HIV load and was effective either early or late in the infection. This study indicates that hunter viruses may halt the progression of the HIV infection by restoring and sustaining high CD4(+) T-cell levels.

Dynamics of an HIV-1 therapy model of fighting a virus with another virus

In this paper, we rigorously analyse an ordinary differential equation system that models fighting the HIV-1 virus with a genetically modified virus. We show that when the basic reproduction ratio ℛ(0)<1, then the infection-free equilibrium E (0) is globally asymptotically stable; when ℛ(0)>1, E (0) loses its stability and there is the single-infection equilibrium E (s). If ℛ(0)∈(1, 1+δ) where δ is a positive constant explicitly depending on system parameters, then the single-infection equilibrium E (s) that is globally asymptotically stable, while when ℛ(0)>1+δ, E (s) becomes unstable and the double-infection equilibrium E (d) comes into existence. When ℛ(0) is slightly larger than 1+δ, E (d) is stable and it loses its stability via Hopf bifurcation when ℛ(0) is further increased in some ways. Through a numerical example and by applying a normal form theory, we demonstrate how to determine the bifurcation direction and stability, as well as the estimates of the amplitudes and the periods of the bifurcated periodic solutions. We also perform numerical simulations which agree with the theoretical results. The approaches we use here are a combination of analysis of characteristic equations, fluctuation lemma, Lyapunov function and normal form theory.

HIV-1 Transmission, Replication Fitness and Disease Progression

Upon transmission, human immunodeficiency virus type 1 (HIV-1) establishes infection of the lymphatic reservoir, leading to profound depletion of the memory CD4+ T cell population despite the induction of the adaptive immune response. The rapid evolution and association of viral variants having distinct characteristics during different stages of infection, the level of viral burden, and rate of disease progression suggest a role for viral variants in this process. Here, we review the literature on HIV-1 variants and disease and discuss the importance of viral fitness for transmission and disease.

Understanding the slow depletion of memory CD4+ T cells in HIV infection

BACKGROUND

The asymptomatic phase of HIV infection is characterised by a slow decline of peripheral blood CD4(+) T cells. Why this decline is slow is not understood. One potential explanation is that the low average rate of homeostatic proliferation or immune activation dictates the pace of a "runaway" decline of memory CD4(+) T cells, in which activation drives infection, higher viral loads, more recruitment of cells into an activated state, and further infection events. We explore this hypothesis using mathematical models.

METHODS AND FINDINGS

Using simple mathematical models of the dynamics of T cell homeostasis and proliferation, we find that this mechanism fails to explain the time scale of CD4(+) memory T cell loss. Instead it predicts the rapid attainment of a stable set point, so other mechanisms must be invoked to explain the slow decline in CD4(+) cells.

CONCLUSIONS

A runaway cycle in which elevated CD4(+) T cell activation and proliferation drive HIV production and vice versa cannot explain the pace of depletion during chronic HIV infection. We summarize some alternative mechanisms by which the CD4(+) memory T cell homeostatic set point might slowly diminish. While none are mutually exclusive, the phenomenon of viral rebound, in which interruption of antiretroviral therapy causes a rapid return to pretreatment viral load and T cell counts, supports the model of virus adaptation as a major force driving depletion.