American Institute of Mathematical Sciences

Advanced
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

Arni S.R. Srinivasa Rao 1, and  Masayuki Kakehashi 2,

1. 

Centre for Ecological Sciences, Indian Institute of Science, Bangalore, 560 012., India
2. 

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.
Keywords: Maximum likelihood method, incubation time distribution., back-calculation.
Mathematics Subject Classification: 92A15,62A1.
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
[1]

Jie Huang, Xiaoping Yang, Yunmei Chen. A fast algorithm for global minimization of maximum likelihood based on ultrasound image segmentation. Inverse Problems & Imaging, 2011, 5 (3) : 645-657. doi: 10.3934/ipi.2011.5.645
[2]

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

Johnathan M. Bardsley. An efficient computational method for total variation-penalized Poisson likelihood estimation. Inverse Problems & Imaging, 2008, 2 (2) : 167-185. doi: 10.3934/ipi.2008.2.167
[4]

Bingsheng He, Xiaoming Yuan. Linearized alternating direction method of multipliers with Gaussian back substitution for separable convex programming. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 247-260. doi: 10.3934/naco.2013.3.247
[5]

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 & Management Optimization, 2017, 13 (5) : 1-21. doi: 10.3934/jimo.2019034
[6]

Yanfei Wang, Qinghua Ma. A gradient method for regularizing retrieval of aerosol particle size distribution function. Journal of Industrial & Management Optimization, 2009, 5 (1) : 115-126. doi: 10.3934/jimo.2009.5.115
[7]

Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control & Related Fields, 2012, 2 (2) : 195-215. doi: 10.3934/mcrf.2012.2.195
[8]

Xuguang Lu. Long time strong convergence to Bose-Einstein distribution for low temperature. Kinetic & Related Models, 2018, 11 (4) : 715-734. doi: 10.3934/krm.2018029
[9]

Bara Kim, Jeongsim Kim. Explicit solution for the stationary distribution of a discrete-time finite buffer queue. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1121-1133. doi: 10.3934/jimo.2016.12.1121
[10]

Albert Fannjiang, Knut Solna. Time reversal of parabolic waves and two-frequency Wigner distribution. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 783-802. doi: 10.3934/dcdsb.2006.6.783
[11]

Johnathan M. Bardsley. A theoretical framework for the regularization of Poisson likelihood estimation problems. Inverse Problems & Imaging, 2010, 4 (1) : 11-17. doi: 10.3934/ipi.2010.4.11
[12]

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 & Management Optimization, 2011, 7 (3) : 593-606. doi: 10.3934/jimo.2011.7.593
[13]

JaEun Ku. Maximum norm error estimates for Div least-squares method for Darcy flows. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1305-1318. doi: 10.3934/dcds.2010.26.1305
[14]

Jiu Ding, Noah H. Rhee. A unified maximum entropy method via spline functions for Frobenius-Perron operators. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 235-245. doi: 10.3934/naco.2013.3.235
[15]

Yunkyong Hyon, José A. Carrillo, Qiang Du, Chun Liu. A maximum entropy principle based closure method for macro-micro models of polymeric materials. Kinetic & Related Models, 2008, 1 (2) : 171-184. doi: 10.3934/krm.2008.1.171
[16]

Liying Wang, Weiguo Zhao, Dan Zhang, Linming Zhao. A geometric inversion algorithm for parameters calculation in Francis turbine. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1373-1384. doi: 10.3934/dcdss.2015.8.1373
[17]

Zhichao Geng, Jinjiang Yuan. Scheduling family jobs on an unbounded parallel-batch machine to minimize makespan and maximum flow time. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1479-1500. doi: 10.3934/jimo.2018017
[18]

Andrei V. Dmitruk, Nikolai P. Osmolovskii. Proof of the maximum principle for a problem with state constraints by the v-change of time variable. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2189-2204. doi: 10.3934/dcdsb.2019090
[19]

Zhiting Xu, Xiao-Qiang Zhao. A vector-bias malaria model with incubation period and diffusion. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2615-2634. doi: 10.3934/dcdsb.2012.17.2615
[20]

Z.G. Feng, K.L. Teo, Y. Zhao. Branch and bound method for sensor scheduling in discrete time. Journal of Industrial & Management Optimization, 2005, 1 (4) : 499-512. doi: 10.3934/jimo.2005.1.499

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (22)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences