# American Institute of Mathematical Sciences

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

 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.
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
 [1] Jinliang Wang, Xiu Dong. Analysis of an HIV infection model incorporating latency age and infection age. Mathematical Biosciences & Engineering, 2018, 15 (3) : 569-594. doi: 10.3934/mbe.2018026 [2] Cristiana J. Silva. Stability and optimal control of a delayed HIV/AIDS-PrEP model. Discrete and Continuous Dynamical Systems - S, 2022, 15 (3) : 639-654. doi: 10.3934/dcdss.2021156 [3] Georgi Kapitanov. A double age-structured model of the co-infection of tuberculosis and HIV. Mathematical Biosciences & Engineering, 2015, 12 (1) : 23-40. doi: 10.3934/mbe.2015.12.23 [4] Hongyong Zhao, Peng Wu, Shigui Ruan. Dynamic analysis and optimal control of a three-age-class HIV/AIDS epidemic model in China. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3491-3521. doi: 10.3934/dcdsb.2020070 [5] Carlota Rebelo, Alessandro Margheri, Nicolas Bacaër. Persistence in some periodic epidemic models with infection age or constant periods of infection. Discrete and Continuous Dynamical Systems - B, 2014, 19 (4) : 1155-1170. doi: 10.3934/dcdsb.2014.19.1155 [6] Yuming Chen, Junyuan Yang, Fengqin Zhang. The global stability of an SIRS model with infection age. Mathematical Biosciences & Engineering, 2014, 11 (3) : 449-469. doi: 10.3934/mbe.2014.11.449 [7] Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595 [8] Liming Cai, Maia Martcheva, Xue-Zhi Li. Epidemic models with age of infection, indirect transmission and incomplete treatment. Discrete and Continuous Dynamical Systems - B, 2013, 18 (9) : 2239-2265. doi: 10.3934/dcdsb.2013.18.2239 [9] Christine K. Yang, Fred Brauer. Calculation of $R_0$ for age-of-infection models. Mathematical Biosciences & Engineering, 2008, 5 (3) : 585-599. doi: 10.3934/mbe.2008.5.585 [10] Hui Miao, Zhidong Teng, Chengjun Kang. Stability and Hopf bifurcation of an HIV infection model with saturation incidence and two delays. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2365-2387. doi: 10.3934/dcdsb.2017121 [11] Hee-Dae Kwon, Jeehyun Lee, Myoungho Yoon. An age-structured model with immune response of HIV infection: Modeling and optimal control approach. Discrete and Continuous Dynamical Systems - B, 2014, 19 (1) : 153-172. doi: 10.3934/dcdsb.2014.19.153 [12] Jinliang Wang, Jiying Lang, Yuming Chen. Global dynamics of an age-structured HIV infection model incorporating latency and cell-to-cell transmission. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3721-3747. doi: 10.3934/dcdsb.2017186 [13] Zhong-Kai Guo, Hai-Feng Huo, Hong Xiang. Analysis of an age-structured model for HIV-TB co-infection. Discrete and Continuous Dynamical Systems - B, 2022, 27 (1) : 199-228. doi: 10.3934/dcdsb.2021037 [14] Yu Ji. Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Mathematical Biosciences & Engineering, 2015, 12 (3) : 525-536. doi: 10.3934/mbe.2015.12.525 [15] Burcu Adivar, Ebru Selin Selen. Compartmental disease transmission models for smallpox. Conference Publications, 2011, 2011 (Special) : 13-21. doi: 10.3934/proc.2011.2011.13 [16] Patrick W. Nelson, Michael A. Gilchrist, Daniel Coombs, James M. Hyman, Alan S. Perelson. An Age-Structured Model of HIV Infection that Allows for Variations in the Production Rate of Viral Particles and the Death Rate of Productively Infected Cells. Mathematical Biosciences & Engineering, 2004, 1 (2) : 267-288. doi: 10.3934/mbe.2004.1.267 [17] Jeng-Huei Chen. An analysis of functional curability on HIV infection models with Michaelis-Menten-type immune response and its generalization. Discrete and Continuous Dynamical Systems - B, 2017, 22 (6) : 2089-2120. doi: 10.3934/dcdsb.2017086 [18] Huizi Yang, Zhanwen Yang, Shengqiang Liu. Numerical threshold of linearly implicit Euler method for nonlinear infection-age SIR models. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022067 [19] Yicang Zhou, Zhien Ma. Global stability of a class of discrete age-structured SIS models with immigration. Mathematical Biosciences & Engineering, 2009, 6 (2) : 409-425. doi: 10.3934/mbe.2009.6.409 [20] Jinliang Wang, Lijuan Guan. Global stability for a HIV-1 infection model with cell-mediated immune response and intracellular delay. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 297-302. doi: 10.3934/dcdsb.2012.17.297

2018 Impact Factor: 1.313