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Title: An age-structured within-host HIV model with T-cell competition
Authors: Wang, Y
Liu, K 
Lou, Y 
Issue Date: Dec-2017
Source: Nonlinear analysis : real world applications, Dec. 2017, v. 38, p. 1-20
Abstract: 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.
Keywords: HIV
Age-structured model
Backward bifurcation
Publisher: Pergamon Press
Journal: Nonlinear analysis : real world applications 
ISSN: 1468-1218
EISSN: 1878-5719
DOI: 10.1016/j.nonrwa.2017.04.002
Rights: © 2017 Elsevier Ltd. All rights reserved.
© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
The following publication Wang, Y., Liu, K., & Lou, Y. (2017). An age-structured within-host HIV model with T-cell competition. Nonlinear Analysis: Real World Applications, 38, 1-20 is available at
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