Modeling HIV Dynamics Under Combination Therapy with Inducers and Antibodies

A mathematical model for HIV dynamics with multiple infections: implications for immune escape

Multiple infections enable the recombination of different strains, which may contribute to viral diversity. How multiple infections affect the competition dynamics between the two types of strains, the wild and the immune escape mutant, remains poorly understood. This study develops a novel mathematical model that includes the two strains, two modes of viral infection, and multiple infections. For the representative double-infection case, the reproductive numbers are derived and global stabilities of equilibria are obtained via the Lyapunov direct method and theory of limiting systems. Numerical simulations indicate similar viral dynamics regardless of multiplicities of infections though the competition between the two strains would be the fiercest in the case of quadruple infections. Through sensitivity analysis, we evaluate the effect of parameters on the set-point viral loads in the presence and absence of multiple infections. The model with multiple infections predict that there exists a threshold for cytotoxic T lymphocytes (CTLs) to minimize the overall viral load. Weak or strong CTLs immune response can result in high overall viral load. If the strength of CTLs maintains at an intermediate level, the fitness cost of the mutant is likely to have a significant impact on the evolutionary dynamics of mutant viruses. We further investigate how multiple infections alter the viral dynamics during the combination antiretroviral therapy (cART). The results show that viral loads may be underestimated during cART if multiple-infection is not taken into account.

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.

Mathematical Analysis of Epidemic Models with Treatment in Heterogeneous Networks

In this paper, we formulate two different network-based epidemic models to investigate the effect of partly effective treatment on disease dynamics. The first network model represents the individuals with heterogeneous number of contacts in a population as choosing a new partner at each moment, whereas the second one assumes the individuals have fixed or stable neighbors. The basic reproduction number [Formula: see text] is computed for each model, using the next generation matrix method. In particular, the critical treatment rate is defined for the model, above which the disease can be eliminated through the treatment. The final epidemic size relations are derived, and the solvability of these implicit equations is studied. In particular, a unique solution of the implicit equation for the final epidemic size is determined, and by rewriting the implicit equation as a suitable fixed point problem, it is proved that the iteration of the fixed point problem converges to the unique solution. Stochastic simulations and numerical simulations, including in comparison with the model outputs and the joint influence of network topology and treatment on the final epidemic size, are conducted to illustrate the theoretical results.

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.

Combination Therapy in Alzheimer’s Disease: Is It Time?

Alzheimer’s disease (AD) is the most common cause of dementia globally. There is increasing evidence showing AD has no single pathogenic mechanism, and thus treatment approaches focusing only on one mechanism are unlikely to be meaningfully effective. With only one potentially disease modifying treatment approved, targeting amyloid-β (Aβ), AD is underserved regarding effective drug treatments. Combining multiple drugs or designing treatments that target multiple pathways could be an effective therapeutic approach. Considering the distinction between added and combination therapies, one can conclude that most trials fall under the category of added therapies. For combination therapy to have an actual impact on the course of AD, it is likely necessary to target multiple mechanisms including but not limited to Aβ and tau pathology. Several challenges have to be addressed regarding combination therapy, including choosing the correct agents, the best time and stage of AD to intervene, designing and providing proper protocols for clinical trials. This can be achieved by a cooperation between the pharmaceutical industry, academia, private research centers, philanthropic institutions, and the regulatory bodies. Based on all the available information, the success of combination therapy to tackle complicated disorders such as cancer, and the blueprint already laid out on how to implement combination therapy and overcome its challenges, an argument can be made that the field has to move cautiously but quickly toward designing new clinical trials, further exploring the pathological mechanisms of AD, and re-examining the previous studies with combination therapies so that effective treatments for AD may be finally found.

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.

Mathematical analysis of an HIV model with latent reservoir, delayed CTL immune response and immune impairment

In this paper, an in-host HIV infection model with latent reservoir, delayed CTL immune response and immune impairment is investigated. By using suitable Lyapunov functions and LaSalle's invariance principle, it is shown that when time delay is equal to zero, the immunity-inactivated reproduction ratio is a threshold determining the global dynamics of the model. By means of the persistence theory for infinite dimensional systems, it is proven that if the immunity-inactivated reproduction ratio is greater than unity, the model is permanent. Choosing time delay as the bifurcation parameter and analyzing the corresponding characteristic equation of the linearized system, the existence of a Hopf bifurcation at the immunity-activated equilibrium is established. Numerical simulations are carried out to illustrate the theoretical results and reveal the effects of some key parameters on viral dynamics.

Effects of periodic intake of drugs of abuse (morphine) on HIV dynamics: Mathematical model and analysis

Drugs of abuse, such as opiates, have been widely associated with diminishing host-immune responses, including suppression of HIV-specific antibody responses. In particular, periodic intake of the drugs of abuse can result in time-varying periodic antibody level within HIV-infected individuals, consequently altering the HIV dynamics. In this study, we develop a mathematical model to analyze the effects of periodic intake of morphine, a widely used opiate. We consider two routes of morphine intake, namely, intravenous morphine (IVM) and slow-release oral morphine (SROM), and integrate several morphine pharmacodynamic parameters into HIV dynamics model. Using our non-autonomous model system we formulate the infection threshold, R_i, for global stability of infection-free equilibrium, which provides a condition for avoiding viral infection in a host. We demonstrate that the infection threshold highly depends on the morphine pharmacodynamic parameters. Such information can be useful in the design of antibody-based vaccines. In addition, we also thoroughly evaluate how alteration of the antibody level due to periodic intake of morphine can affect the viral load and the CD4 count in HIV infected drug abusers.