Mathematical models based on ordinary differential equations (ODE) have had significant impact on understanding HIV disease dynamics and optimizing patient treatment. A model that characterizes the essential disease dynamics can be used for prediction only if the model parameters are identifiable from clinical data. Most previous parameter identification studies for HIV have used sparsely sampled data from the decay phase following the introduction of therapy. In this paper, model parameters are identified from frequently sampled viral-load data taken from ten patients enrolled in the previously published AutoVac HAART interruption study, providing between 69 and 114 viral load measurements from 3–5 phases of viral decay and rebound for each patient. This dataset is considerably larger than those used in previously published parameter estimation studies. Furthermore, the measurements come from two separate experimental conditions, which allows for the direct estimation of drug efficacy and reservoir contribution rates, two parameters that cannot be identified from decay-phase data alone. A Markov-Chain Monte-Carlo method is used to estimate the model parameter values, with initial estimates obtained using nonlinear least-squares methods. The posterior distributions of the parameter estimates are reported and compared for all patients.

A model of reservoir activation and viral replication is introduced accounting for the production of 2-LTR HIV-1 DNA circles following antiviral intensification with the HIV integrase inhibitor raltegravir, considering contributions of de novo infection events and exogenous sources of infected cells, including quiescent infected cell activation. The model shows that a monotonic increase in measured 2-LTR concentration post intensification is consistent with limited de novo infection primarily maintained by sources of infected cells unaffected by raltegravir, such as quiescent cell activation, while a transient increase in measured 2-LTR concentration is consistent with significant levels of efficient (R0 > 1) de novo infection. The model is validated against patient data from the INTEGRAL study and is shown to have a statistically significant fit relative to the null hypothesis of random measurement variation about a mean. We obtain estimates and confidence intervals for the model parameters, including 2-LTR half-life. Seven of the 13 patients with detectable 2-LTR concentrations from the INTEGRAL study have measured 2-LTR dynamics consistent with significant levels of efficient replication of the virus prior to treatment intensification.

Combination Antiretroviral Therapy (cART) can suppress plasma HIV below the limit of detection in normal assays. Recently reported results suggest that viral replication may continue in some patients, despite undetectable levels in the blood. It has been suggested that the appearance of the circularized episomal HIV DNA artifact 2-LTR following treatment intensification with the integrase inhibitor raltegravir is a marker of ongoing viral replication. Other work has suggested that lymphoid organs may be a site of reduced antiviral penetration and increased viral production. In this study we model the hypothesis that this ongoing replication occurs in lymphoid follicle sanctuary sites and investigate the patterns of 2-LTR formation expected after raltegravir application. Experimental data is used to estimate the reaction and diffusion parameters in the model, and Monte-Carlo simulations are used to explore model behavior subject to variation in these rates. The results suggest that conditions for the formation of an observed transient peak in 2-LTR formation following raltegravir intensification include a sanctuary site diameter larger than 0.2 mm, a viral basic reproductive ratio within the site larger than 1, and a total volume of active sanctuary sites above 20 mL. Significant levels of uncontrolled replication can occur in the sanctuary sites without measurable changes in the plasma viral load. By contrast, subcritical replication (where the basic reproductive ratio of the virus is less than 1 in all sites) always results in monotonic increases of measured 2-LTR following raltegravir intensification, occurring at levels below the limit of detection.

The development of resistant strains of HIV is the most significant barrier to effective long-term treatment of HIV infection. The most common causes of resistance development are patient noncompliance and pre-existence of resistant strains. In this paper, methods of antiviral regimen switching are developed that minimize the risk of pre-existing resistant virus emerging during therapy switches necessitated by virological failure. Two distinct cases are considered; a single previous virological failure and multiple virological failures. These methods use optimal control approaches on experimentally verified mathematical models of HIV strain competition and statistical models of resistance risk. It is shown that, theoretically, order-of-magnitude reduction in risk can be achieved, and multiple previous virological failures enable greater success of these methods in reducing the risk of subsequent treatment failures.

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Since 1996, the National Institutes of Health and other organizations have recommended offering Highly Active Antiretroviral Therapy (HAART) to all patients infected with HIV. Although HAART provides a powerful strategy for HIV treatment, it does not prevent completely the development of multi-drug resistant strains, and drug resistance is the primary reason for treatment failure. A better control of drug-resistance risk is critical for the success of long-term antiviral therapy in HIV patients. Recent research focuses on how to develop new drugs, but little has been done to control resistance risk by using an appropriate treatment regime. In this paper, we propose a generalized multi-strain model of HIV evolution with viral mutations. Based on this model, we suggest a drug switching strategy to minimize resistance risk and preserve long-term control of the HIV infection for the case in which the patient only has one kind of drug-resistance virus. Though simulations, this model can also be used for detecting and minimizing the resistance risk for the patients who develops multiple drugregimen resistance.

bWe present a simple computational model of measurement accuracy for single-copy sensitivity assays (SCA) of HIV RNA that was developed from first principles. The model shows that the SCA is significantly right-skewed. Measured virus concentrations of 1 and 10 virions/ml had overlapping 95% confidence intervals and were statistically indistinguishable.

Evolution has long been understood as the driving force for many problems of medical interest. The evolution of drug resistance in HIV and bacterial infections is recognized as one of the most significant emerging problems in medicine. In cancer therapy, the evolution of resistance to chemotherapeutic agents is often the differentiating factor between effective therapy and disease progression or death. Interventions to manage the evolution of resistance have, up to this point, been based on steady-state analysis of mutation and selection models. In this paper, we review the mathematical methods applied to studying evolution of resistance in disease. We present a broad review of several classical applications of mathematical modeling of evolution, and review in depth two recent problems which demonstrate the potential for interventions which exploit the dynamic behavior of resistance evolution models. The first problem addresses the problem of sequential treatment failures in HIV; we present a review of our recent publications addressing this problem. The second problem addresses a novel approach to gene therapy for pancreatic cancer treatment, where selection is used to encourage optimal spread of susceptibility genes through a target tumor, which is then eradicated during a second treatment phase. We review the recent in Vitro laboratory work on this topic, present a new mathematical model to describe the treatment process, and show why model-based approaches will be necessary to successfully implement this novel and promising approach.