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Title: Age-structured within-host HIV dynamics with multiple target cells
Authors: Wang, X
Lou, YJ 
Song, XY
Issue Date: Jan-2017
Source: Studies in applied mathematics, Jan. 2017, v. 138, no. 1, p. 43-76
Abstract: Human immunodeficiency virus (HIV) can infect various types of cell populations such as CD4+ T cells and macrophages. The heterogeneity of these target cells implies different birth, death, infection rates, and so on. To investigate the within-host dynamics of HIV which can infect n different types of target cells, a theoretical model with infection-age structure for each type of target cells and a general nonlinear incidence rate is proposed in this manuscript. The model, in the form of a hyperbolic system of partial differential equations (PDE) for infected target cells coupled with several ordinary differential equations, is shown to be biologically reasonable with the establishment of existence, positivity, and boundedness of solutions. Although the PDE form poses novel challenges to theoretical investigation, rigorous analysis is performed to show the uniform persistence of the virus when the basic reproduction number is greater than one. Furthermore, by constructing suitable Lyapunov functionals, we show that the infection-free steady state is globally asymptotically stable when the basic reproduction number is less than unity, while the positive steady state is globally asymptotically stable when the basic reproduction number is greater than one.
Publisher: Wiley-Blackwell
Journal: Studies in applied mathematics 
ISSN: 0022-2526
EISSN: 1467-9590
DOI: 10.1111/sapm.12135
Rights: ©2016 Wiley Periodicals, Inc., A Wiley Company
This is the peer reviewed version of the following article: Wang, X., Lou, Y., & Song, X. (2017). Age‐Structured Within‐Host HIV Dynamics with Multiple Target Cells. Studies in Applied Mathematics, 138(1), 43-76, which has been published in final form at https://doi.org/10.1111/sapm.12135. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
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