2005, 2(2): 263-277. doi: 10.3934/mbe.2005.2.263

Incubation-time distribution in back-calculation applied to HIV/AIDS data in India


Centre for Ecological Sciences, Indian Institute of Science, Bangalore, 560 012., India


Institute of Health Science, Faculty of Medicine, Hiroshima University, Hiroshima, 734-8551, Japan

Received  June 2004 Revised  March 2005 Published  March 2005

In this article, HIV incidence density is estimated from prevalence data and then used together with reported cases of AIDS to estimate incubation-time distribution. We used deconvolution technique and maximum likelihood method to estimate parameters. The effect of truncation in hazard was also examined. The mean and standard deviation obtained with the Weibull assumption were 12.9 and 3.0 years, respectively. The estimation seemed useful to investigate distribution of time between report of HIV infection and that of AIDS development. If we assume truncation, the optimum truncating point was sensitive to the HIV growth assumed. This procedure was applied to US data for validating the results obtained from the Indian data. The results show that method works well.
Citation: Arni S.R. Srinivasa Rao, Masayuki Kakehashi. Incubation-time distribution in back-calculation applied to HIV/AIDS data in India. Mathematical Biosciences & Engineering, 2005, 2 (2) : 263-277. doi: 10.3934/mbe.2005.2.263

Jie Huang, Xiaoping Yang, Yunmei Chen. A fast algorithm for global minimization of maximum likelihood based on ultrasound image segmentation. Inverse Problems and Imaging, 2011, 5 (3) : 645-657. doi: 10.3934/ipi.2011.5.645


Saroja Kumar Singh. Moderate deviation for maximum likelihood estimators from single server queues. Probability, Uncertainty and Quantitative Risk, 2020, 5 (0) : 2-. doi: 10.1186/s41546-020-00044-z


R.L. Sheu, M.J. Ting, I.L. Wang. Maximum flow problem in the distribution network. Journal of Industrial and Management Optimization, 2006, 2 (3) : 237-254. doi: 10.3934/jimo.2006.2.237


Johnathan M. Bardsley. An efficient computational method for total variation-penalized Poisson likelihood estimation. Inverse Problems and Imaging, 2008, 2 (2) : 167-185. doi: 10.3934/ipi.2008.2.167


Bingsheng He, Xiaoming Yuan. Linearized alternating direction method of multipliers with Gaussian back substitution for separable convex programming. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 247-260. doi: 10.3934/naco.2013.3.247


Ming Huang, Cong Cheng, Yang Li, Zun Quan Xia. The space decomposition method for the sum of nonlinear convex maximum eigenvalues and its applications. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1885-1905. doi: 10.3934/jimo.2019034


Ting Hu. Kernel-based maximum correntropy criterion with gradient descent method. Communications on Pure and Applied Analysis, 2020, 19 (8) : 4159-4177. doi: 10.3934/cpaa.2020186


Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control and Related Fields, 2012, 2 (2) : 195-215. doi: 10.3934/mcrf.2012.2.195


Yanfei Wang, Qinghua Ma. A gradient method for regularizing retrieval of aerosol particle size distribution function. Journal of Industrial and Management Optimization, 2009, 5 (1) : 115-126. doi: 10.3934/jimo.2009.5.115


Xuguang Lu. Long time strong convergence to Bose-Einstein distribution for low temperature. Kinetic and Related Models, 2018, 11 (4) : 715-734. doi: 10.3934/krm.2018029


Bara Kim, Jeongsim Kim. Explicit solution for the stationary distribution of a discrete-time finite buffer queue. Journal of Industrial and Management Optimization, 2016, 12 (3) : 1121-1133. doi: 10.3934/jimo.2016.12.1121


Albert Fannjiang, Knut Solna. Time reversal of parabolic waves and two-frequency Wigner distribution. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : 783-802. doi: 10.3934/dcdsb.2006.6.783


Johnathan M. Bardsley. A theoretical framework for the regularization of Poisson likelihood estimation problems. Inverse Problems and Imaging, 2010, 4 (1) : 11-17. doi: 10.3934/ipi.2010.4.11


Liying Wang, Weiguo Zhao, Dan Zhang, Linming Zhao. A geometric inversion algorithm for parameters calculation in Francis turbine. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1373-1384. doi: 10.3934/dcdss.2015.8.1373


Danfeng Pang, Yanni Xiao, Xiao-Qiang Zhao. A cross-infection model with diffusion and incubation period. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2021316


JaEun Ku. Maximum norm error estimates for Div least-squares method for Darcy flows. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1305-1318. doi: 10.3934/dcds.2010.26.1305


Jiu Ding, Noah H. Rhee. A unified maximum entropy method via spline functions for Frobenius-Perron operators. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 235-245. doi: 10.3934/naco.2013.3.235


Yunkyong Hyon, José A. Carrillo, Qiang Du, Chun Liu. A maximum entropy principle based closure method for macro-micro models of polymeric materials. Kinetic and Related Models, 2008, 1 (2) : 171-184. doi: 10.3934/krm.2008.1.171


Yutaka Sakuma, Atsushi Inoie, Ken’ichi Kawanishi, Masakiyo Miyazawa. Tail asymptotics for waiting time distribution of an M/M/s queue with general impatient time. Journal of Industrial and Management Optimization, 2011, 7 (3) : 593-606. doi: 10.3934/jimo.2011.7.593


Zhichao Geng, Jinjiang Yuan. Scheduling family jobs on an unbounded parallel-batch machine to minimize makespan and maximum flow time. Journal of Industrial and Management Optimization, 2018, 14 (4) : 1479-1500. doi: 10.3934/jimo.2018017

2018 Impact Factor: 1.313


  • PDF downloads (58)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]