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In this paper, we develop mathematical models that include impairment of B-cell functions in order to study HIV dynamics. Two forms of the incidence rate have been considered, bilinear and general nonlinear. Three types of infected cells have been incorporated into the models, namely latently infected, short-lived productively infected and long-lived productively infected. The models have at most two equilibria, whose existence is characterized by means of the basic reproduction number $R_0$. The global stability of each equilibrium is proven by using the Lyapunov method. The effects of impairment of B-cell functions and of antiviral treatment on the human immunodeficiency virus (HIV) dynamics are studied. We have shown that if the functions of B-cell are impaired, then the concentration of HIV increases in the plasma. Moreover, we have determined the minimal drug efficacy which is required to reduce the concentration of HIV particles to a lower level. We have shown that a more accurate computation of drug efficacy can be performed by using our proposed model. Our theoretical results are illustrated by means of numerical simulations.

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.

In this paper, we study the global properties of a human immunodeficiency virus (HIV) infection model with cytotoxic T lymphocytes (CTL) immune response. The model is a six-dimensional that describes the interaction of the HIV with two classes of target cells, CD4⁺ T cells and macrophages. The infection rate is given by saturation functional response. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic infection reproduction number R₀ and the immune response activation number . We have proven that if R₀ ≤ 1, then the uninfected steady state is globally asymptotically stable (GAS), if , then the infected steady state without CTL immune response is GAS, and if , then the infected steady state with CTL immune response is GAS.

In this paper, we have studied about the sensitivity analysis of the human immunodeficiency virus (HIV) protease inhibitor (PI) model and estimated the length of the delay. We have fabricated an HIV PI model accompanied with humoral immunity. Stability analysis of the constructed model about its steady states has been deliberated. We have evaluated some numerical simulations for PI model with humoral immunity by using the existing patient data.

There have been substantial interests in investigating HIV dynamics for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. However, it is difficult to establish a relationship between pharmacokinetics (PK) and antiviral response due to too many confounding factors related to antiviral response during the treatment process. In this article, a mechanism-based dynamic model for HIV infection with intervention by antiretroviral therapies is proposed. In this model, we directly incorporate drug concentration, adherence and drug susceptibility into a function of treatment efficacy defined as an inhibition rate of virus replication. In order to focus our attention on estimating dynamic parameters for all subjects, we investigate a Bayesian approach under a framework of the hierarchical Bayesian (mixed-effects) model. The proposed methods and models not only can help to alleviate the difficulty in identifiability, but also can flexibly deal with sparse and unbalanced longitudinal data. The viral dynamic parameters estimated from the proposed method are, thus, more accurate since the variations in PK, adherence and drug resistance have been considered in the model.

In this chapter, we have assessed the time to development of drug resistance in HIV-infected individuals treated with antiviral drugs by using longitudinal viral load HIV-1 counts. Through log transformed data of HIV virus counts over time, we have assumed a linear changing-point model and developed procedures to estimate the unknown parameters by using the Bayesian approach. We have applied the method and procedure to the data generated by the ACTG 315 involving treatment by the drug combination (3TC, AZT and Ritonavir). Our analysis showed that the mean time to the first changing point (i.e. the time the macrophage and long-lived cells began to release HIV particles) was around 15 days whereas the time to development of drug resistance by HIV was around 75 days. The Bayesian HPD intervals for these changing points are given by (8.7,21.3) and (42,108) respectively. This analysis indicated that if we use the combination of three drugs involving 2 NRTI inhibitors (3TC and AZT) and 1 PI inhibitor (Ritonavir) to treat HIV-infected individuals, in about two and half months it would be beneficial to change drugs to avoid the problem of drug resistance.