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Recent studies demonstrate that resource competition is an essential component of T-cell proliferation in HIV progression, which can contribute instructively to the disease development. In this paper, we formulate an age-structured within-host HIV model, in the form of a hyperbolic partial differential equation (PDE) for infected target cells coupled with two ordinary differential equations for uninfected T-cells and the virions, to explore the effects of both the T-cell competition and viral shedding variations on the viral dynamics. The basic reproduction number is derived for a general viral production rate which determines the local stability of the infection-free equilibrium. Two special forms of viral production rates, which are extensively investigated in previous literature, the delayed exponential distribution and a step function rate, are further investigated, where the original system can be reduced into systems of delay differential equations. It is confirmed that there exists a unique positive equilibrium for two special viral production rates when the basic reproduction number is greater than one. However, the model exhibits the phenomenon of backward bifurcation, where two positive steady states coexist with the infection-free equilibrium when the basic reproduction number is less than one. [ABSTRACT FROM AUTHOR]

Abstract: The HIV/AIDS epidemic is a serious public health challenge in South Africa. In this paper, a simple deterministic HIV/AIDS model incorporating condom use, sexual partner acquisition, behavior change and treatment as HIV/AIDS control strategies is formulated using a system of ordinary differential equations with the object of applying it to the current South African situation. Firstly, a theoretical analysis of the model is presented. The analysis of the model shows that the disease free equilibrium point is globally asymptotically stable for the epidemic threshold (the model reproduction number) less than unit and unstable when this threshold is greater than unit. A unique endemic equilibrium, whose local stability near the threshold , is determined using the center manifold theory, is shown to be locally asymptotically stable for . Global stability of the endemic equilibrium is shown for a special case whenever . Secondly, the model is fitted to data from UNAIDS/WHO on HIV/AIDS in South Africa. Based on the fit to the prevalence data, projections are made beyond 2007 on the course of the epidemic for various levels of interventions. The results compare very well with other research outcomes on the HIV/AIDS epidemic in South Africa. Projections are made to track the changes in the number of individuals who will be under treatment, an important group as far as public health planning is concerned. The epidemiological implications of such projections on public health planning and management are discussed. [Copyright &y& Elsevier]

Abstract: In this paper, we have considered a nonautonomous stage-structured HIV/AIDS epidemic model having two stages of the period of infection according to the developing progress of infection before AIDS defined in, with varying total population size and distributed time delay to become infectious. The infected persons in the different stages have different abilities of transmitting disease. By all kinds of treatment methods, some people with the symptomatic stages can be transformed into asymptomatic stages. Here, we have established some sufficient conditions on the permanence and extinction of the disease by using the inequality analytical technique. We have obtained the explicit formula of the eventual lower bounds of infected persons. We have introduced some new threshold values and and further obtained that the disease will be permanent when and the disease will be going extinct when . By the Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Also, we have observed that the time delay decreases the lower bounds of the infective and full-blown AIDS group. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the global properties of a class of human immunodeficiency virus (HIV) models. The basic model is a 5-dimensional nonlinear ODEs that describes the interaction of the HIV with two target cells, CD4+ T cells and macrophages. An HIV model with exposed state and a model with nonlinear incidence rate are also analyzed. Lyapunov functions are constructed to establish the global asymptotic stability of the uninfected and infected steady states. We have proven that if the basic reproduction number is less than unity, then the uninfected steady state is globally asymptotically stable. If (or if the infected steady state exists), then the infected steady state is globally asymptotically stable. In a control system framework, we have shown that the HIV model incorporating the effect of Highly Active AntiRetroviral Therapy (HAART) is globally asymptotically controllable to the uninfected steady state. [Copyright &y& Elsevier]