# American Institute of Mathematical Sciences

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

 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.
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
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