Treatment of HIV infection has traditionally consisted of antiretroviral therapy (ART), a regimen of pharmaceutical treatments that often produces unwanted physical side effects and can become costly over long periods of time. Motivated by a way to control the spread of HIV in the body without the need for large quantities of medicine, researchers have explored treatment methods which rely on stimulating an individual's immune response, such as the cytotoxic lymphocyte (CTL) response, in addition to the usage of antiretroviral drugs. This paper investigates theoretically and numerically the effect of immune effectors in modeling HIV pathogenesis, our results suggest the significant impact of the immune response on the control of the virus during primary infection. Qualitative aspects (including positivity, stability, uncertainty, and sensitivity analysis) are addressed. Additionally, by introducing drug therapy, we analyze numerically the model to assess the effect of treatment. Our results show that the inclusion of the CTL compartment produces a higher rebound for an individual's healthy helper T-cell compartment than does drug therapy alone. Furthermore, we quantitatively characterize successful drugs or drug combination scenarios.
The modeling of the surface of viscosity in composition and temperature at atmospheric pressure for methanol−water and acetonitrile−water was performed by interconnecting various elementary functions and testing them in a systematic manner to minimize the least-squares error. The systematic approach involved developing expressions that were the sum or product of elementary functions in temperature and composition, then visually observing their fit and quantitating the error. To reduce the error, transformation of the data using elementary functions was necessary to create a modified surface simpler in form. For MeOH−H2O, the least-squares error was 0.6 and 0.01 for untransformed data and transformed data, respectively. Similarly, for ACN−H2O, the error was 0.3 and 0.008 for untransformed and transformed data, respectively. The expression describing the viscosity−composition−temperature relationship for both the transformed and untransformed data was a quadratic in x with exponential functions of T as coefficients where T° is a nondimensionalizing term of value one. The transformed temperature is log(T/T°) + 2, while the transformed viscosity was η1/8.
In treating the human immunodeficiency virus (HIV) infection, strict adherence to drug therapy is crucial for maintaining a low viral load, but the high dosages required for this often have toxic side effects which make perfect adherence to antiretroviral therapy (ART) unsustainable. Even in the presence of drug therapy, ongoing viral replication can lead to the emergence of drug resistance. In this paper, we investigate the effect of immune effectors in modelling HIV pathogenesis during ART, showing a higher rebound for healthy T-cell concentration than drug therapy alone. A periodic model of bang-bang type and a pharmacokinetic model are employed to estimate the drug efficacies. We numerically investigate how time-varying drug efficacy due to drug dosing regimen and/or suboptimal adherence affects the antiviral response and how it affects the emergence of drug resistance. Moreover, we qualitatively characterize successful drugs or drug combination scenarios.
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