Modeling and prediction of HIV in China: transmission rates structured by infection ages
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1.
Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049
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2.
State Key Laboratory for Infectious Disease Prevention and Control and National Center for AIDS/STD Control and Prevention, Chinese Center for Disease Control and Prevention, 27 Nanwei Road, Xuanwu District, Beijing 100050
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3.
Department of Applied Mathematics, College of Science, Xian Jiaotong University, Xian 710049
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4.
Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, 710049
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5.
Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3
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Received:
01 September 2007
Accepted:
29 June 2018
Published:
01 March 2008
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MSC :
Primary: 92D30; Secondary: 39A11.
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HIV transmission process involves a long incubation and infection
period, and the transmission rate varies greatly with infection stage. Conse-
quently, modeling analysis based on the assumption of a constant transmission
rate during the entire infection period yields an inaccurate description of HIV
transmission dynamics and long-term projections. Here we develop a general
framework of mathematical modeling that takes into account this heterogeneity
of transmission rate and permits rigorous estimation of important parameters
using a regression analysis of the twenty-year reported HIV infection data in
China. Despite the large variation in this statistical data attributable to the
knowledge of HIV, surveillance efforts, and uncertain events, and although the
reported data counts individuals who might have been infected many years
ago, our analysis shows that the model structured on infection age can assist
us in extracting from this data set very useful information about transmission
trends and about effectiveness of various control measures.
Citation: Yicang Zhou, Yiming Shao, Yuhua Ruan, Jianqing Xu, Zhien Ma, Changlin Mei, Jianhong Wu. Modeling and prediction of HIV in China: transmission rates structured by infection ages[J]. Mathematical Biosciences and Engineering, 2008, 5(2): 403-418. doi: 10.3934/mbe.2008.5.403
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Abstract
HIV transmission process involves a long incubation and infection
period, and the transmission rate varies greatly with infection stage. Conse-
quently, modeling analysis based on the assumption of a constant transmission
rate during the entire infection period yields an inaccurate description of HIV
transmission dynamics and long-term projections. Here we develop a general
framework of mathematical modeling that takes into account this heterogeneity
of transmission rate and permits rigorous estimation of important parameters
using a regression analysis of the twenty-year reported HIV infection data in
China. Despite the large variation in this statistical data attributable to the
knowledge of HIV, surveillance efforts, and uncertain events, and although the
reported data counts individuals who might have been infected many years
ago, our analysis shows that the model structured on infection age can assist
us in extracting from this data set very useful information about transmission
trends and about effectiveness of various control measures.
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