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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. [ABSTRACT FROM AUTHOR]

Simple models of therapy for viral diseases such as hepatitis C virus (HCV) or human immunodeficiency virus assume that, once therapy is started, the drug has a constant effectiveness. More realistic models have assumed either that the drug effectiveness depends on the drug concentration or that the effectiveness varies over time. Here a previously introduced varying-effectiveness (VE) model is studied mathematically in the context of HCV infection. We show that while the model is linear, it has no closed-form solution due to the time-varying nature of the effectiveness. We then show that the model can be transformed into a Bessel equation and derive an analytic solution in terms of modified Bessel functions, which are defined as infinite series, with time-varying arguments. Fitting the solution to data from HCV infected patients under therapy has yielded values for the parameters in the model. We show that for biologically realistic parameters, the predicted viral decay on therapy is generally biphasic and resembles that predicted by constant-effectiveness (CE) models. We introduce a general method for determining the time at which the transition between decay phases occurs based on calculating the point of maximum curvature of the viral decay curve. For the parameter regimes of interest, we also find approximate solutions for the VE model and establish the asymptotic behavior of the system. We show that the rate of second phase decay is determined by the death rate of infected cells multiplied by the maximum effectiveness of therapy, whereas the rate of first phase decline depends on multiple parameters including the rate of increase of drug effectiveness with time. [ABSTRACT FROM AUTHOR]

Several studies have proven oseltamivir to be efficient in reducing influenza viral titer and symptom intensity. However, the usefulness of oseltamivir can be compromised by the emergence and spread of drug-resistant virus. The selective pressure exerted by different oseltamivir therapy regimens have received little attention. Combining models of drug pharmacokinetics, pharmacodynamics, viral kinetics and symptom dynamics, we explored the efficacy of oseltamivir in reducing both symptoms (symptom efficacy) and viral load (virological efficacy). We simulated samples of 1000 subjects using previously estimated between-subject variability in viral and symptom dynamic parameters to describe the observed heterogeneity in a patient population. We simulated random mutations conferring resistance to oseltamivir. We explored the effect of therapy initiation time, dose, intake frequency and therapy duration on influenza infection, illness dynamics, and emergence of viral resistance. Symptom and virological efficacies were strongly associated with therapy initiation time. The proportion of subjects shedding resistant virus was 27-fold higher when prophylaxis was initiated during the incubation period compared with no treatment. It fell to below 1% when treatment was initiated after symptom onset for twice-a-day intakes. Lower doses and prophylaxis regimens led to lower efficacies and increased risk of resistance emergence. We conclude that prophylaxis initiated during the incubation period is the main factor leading to resistance emergence. [ABSTRACT FROM AUTHOR]