NDLI: A model of HIV-1 infection with two time delays: mathematical analysis and comparison with patient data

Content Provider	PubMed Central
Author	Pawelek, Kasia A. Liu, Shengqiang Pahlevani, Faranak Rong, Libin
Copyright Year	2011
Abstract	Mathematical models have made considerable contributions to our understanding of HIV dynamics. Introducing time delays to HIV models usually brings challenges to both mathematical analysis of the models and comparison of model predictions with patient data. In this paper, we incorporate two delays, one the time needed for infected cells to produce virions after viral entry and the other the time needed for the adaptive immune response to emerge to control viral replication, into an HIV-1 model. We begin model analysis with proving the positivity and boundedness of the solutions, local stability of the infection-free and infected steady states, and uniform persistence of the system. By developing a few Lyapunov functionals, we obtain conditions ensuring global stability of the steady states. We also fit the model including two delays to viral load data from 10 patients during primary HIV-1 infection and estimate parameter values. Although the delay model provides better fits to patient data (achieving a smaller error between data and modeling prediction) than the one without delays, we could not determine which one is better from the statistical standpoint. This highlights the need of more data sets for model verification and selection when we incorporate time delays into mathematical models to study virus dynamics.
Related Links	http://dx.doi.org/10.1016/j.mbs.2011.11.002
Ending Page	109
Page Count	12
Starting Page	98
File Format	PDF
ISSN	00255564
e-ISSN	18793134
Journal	Mathematical Biosciences
Issue Number	1
Volume Number	235
Language	English
Publisher Date	2012-01-01
Access Restriction	Open
Subject Keyword	Biochemistry, Genetics and Molecular Biology(all) Modelling and Simulation Statistics and Probability Immunology and Microbiology(all) Applied Mathematics Agricultural and Biological Sciences(all) Medicine(all) Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistics and Probability Immunology and Microbiology Medicine Biochemistry, Genetics and Molecular Biology Agricultural and Biological Sciences Modeling and Simulation

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