Study On The Global Behavior Of HIV - Based Age - Structured HIV Model

Recent studies reveal that cell-to-cell transmission via formation of virological synapses can contribute significantly to virus spread, and hence, may play a more important role than virus-to-cell infection in some situations. In this paper, agestructured models can be employed to study the variations with regard to infection age in modeling the death rate and virus production rate of infected cells. We mainly study that two classes of infection model, one class concerned that the influence of cell-to-cell infection of the host; while others concerned with a within-host virus model incorporating latency and cellto- cell transmission. Considering the above characteristics for within-host dynamics models of HIV is will be more complex than the previous ODEs and FDEs equation model, we formulate a hybrid dynamic model of ODEs and PDEs equations to explore the effects of the two infection modes in viral production and spread.In mathematical analysis, we have addressing the relative compactness and persistence of the solution semiflow, and existence of a global attractor. By the traditional differential equations to find the subtle kernel function and construction of Lyapunov functions, we show that the global attractor actually consists of an singleton and its global asymptotic stability.