TY - JOUR
T1 - A model of HIV-1 infection with two time delays
T2 - Mathematical analysis and comparison with patient data
AU - Pawelek, Kasia A.
AU - Liu, Shengqiang
AU - Pahlevani, Faranak
AU - Rong, Libin
N1 - Funding Information:
Portions of this work were performed during the first three authors’ visit to the Fields Institute (Summer 2010 Thematic Program on the Mathematics of Drug Resistance in Infectious Diseases). They would like to acknowledge the hospitality received there. The work is supported in part by the NSF Grant DMS-1122290 and NIH P30-EB011339 (LR), the NNSF of China (No. 61075037 ), the Fundamental Research Funds for the Central Universities (No. HIT.NSRIF.2010052 ) and Program of Excellent Team in Harbin Institute of Technology (SL). The authors also thank the referees for the comments that improved this manuscript.
PY - 2012/1
Y1 - 2012/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.mbs.2011.11.002
DO - 10.1016/j.mbs.2011.11.002
M3 - Article
C2 - 22108296
AN - SCOPUS:84857796637
SN - 0025-5564
VL - 235
SP - 98
EP - 109
JO - Mathematical Biosciences
JF - Mathematical Biosciences
IS - 1
ER -
