# 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] 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 [3] Carlota Rebelo, Alessandro Margheri, Nicolas Bacaër. Persistence in some periodic epidemic models with infection age or constant periods of infection. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1155-1170. doi: 10.3934/dcdsb.2014.19.1155 [4] 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 [5] 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 [6] Liming Cai, Maia Martcheva, Xue-Zhi Li. Epidemic models with age of infection, indirect transmission and incomplete treatment. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2239-2265. doi: 10.3934/dcdsb.2013.18.2239 [7] 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 [8] Hui Miao, Zhidong Teng, Chengjun Kang. Stability and Hopf bifurcation of an HIV infection model with saturation incidence and two delays. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2365-2387. doi: 10.3934/dcdsb.2017121 [9] Hee-Dae Kwon, Jeehyun Lee, Myoungho Yoon. An age-structured model with immune response of HIV infection: Modeling and optimal control approach. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 153-172. doi: 10.3934/dcdsb.2014.19.153 [10] Jinliang Wang, Jiying Lang, Yuming Chen. Global dynamics of an age-structured HIV infection model incorporating latency and cell-to-cell transmission. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3721-3747. doi: 10.3934/dcdsb.2017186 [11] 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 [12] 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 [13] 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 [14] Jeng-Huei Chen. An analysis of functional curability on HIV infection models with Michaelis-Menten-type immune response and its generalization. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2089-2120. doi: 10.3934/dcdsb.2017086 [15] Jinliang Wang, Lijuan Guan. Global stability for a HIV-1 infection model with cell-mediated immune response and intracellular delay. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 297-302. doi: 10.3934/dcdsb.2012.17.297 [16] 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 [17] Yu Yang, Shigui Ruan, Dongmei Xiao. Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function. Mathematical Biosciences & Engineering, 2015, 12 (4) : 859-877. doi: 10.3934/mbe.2015.12.859 [18] Miguel Atencia, Esther García-Garaluz, Gonzalo Joya. The ratio of hidden HIV infection in Cuba. Mathematical Biosciences & Engineering, 2013, 10 (4) : 959-977. doi: 10.3934/mbe.2013.10.959 [19] Cristiana J. Silva, Delfim F. M. Torres. A TB-HIV/AIDS coinfection model and optimal control treatment. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4639-4663. doi: 10.3934/dcds.2015.35.4639 [20] Cristiana J. Silva, Delfim F. M. Torres. Modeling and optimal control of HIV/AIDS prevention through PrEP. Discrete & Continuous Dynamical Systems - S, 2018, 11 (1) : 119-141. doi: 10.3934/dcdss.2018008

2018 Impact Factor: 1.313