American Institute of Mathematical Sciences

Advanced
2008, 5(2): 403-418. doi: 10.3934/mbe.2008.5.403

Modeling and prediction of HIV in China: transmission rates structured by infection ages

Yicang Zhou 1, , Yiming Shao 2, , Yuhua Ruan 2, , Jianqing Xu 2, , Zhien Ma 3, , Changlin Mei 4, and  Jianhong Wu 5,

1. 

Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China
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, China, China, China
3. 

Department of Applied Mathematics, College of Science, Xian Jiaotong University, Xian 710049
4. 

Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, 710049, China
5. 

Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3

Received  September 2007 Revised  November 2007 Published  March 2008

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.
Keywords: compartmental models, stability., HIV/AIDS, infection age.
Mathematics Subject Classification: Primary: 92D30; Secondary: 39A1.
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. Mathematical Biosciences & Engineering, 2008, 5 (2) : 403-418. doi: 10.3934/mbe.2008.5.403
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