# American Institute of Mathematical Sciences

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Modeling dynamic changes in type 1 diabetes progression: Quantifying $\beta$-cell variation after the appearance of islet-specific autoimmune responses
2009, 6(4): 779-813. doi: 10.3934/mbe.2009.6.779

## HIV/AIDS epidemic in India and predicting the impact of the national response: Mathematical modeling and analysis

 1 Mathematical Institute, Centre for Mathematical Biology, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, United Kingdom 2 Department of Medicine, Christian Medical College, Vellore, India 3 Member, National AIDS Control Programmme Planning Team, Currently with Global AIDS Program, US Centers for Disease Control and Prevention, American Embassy New Delhi, India 4 Centre for Mathematical Biology, Mathematical Institute, University of Oxford, OX1 3LB Oxford

Received  June 2007 Revised  April 2009 Published  September 2009

After two phases of AIDS control activities in India, the third phase of the National AIDS Control Programme (NACP III) was launched in July 2007. Our focus here is to predict the number of people living with HIV/AIDS (PLHA) in India so that the results can assist the NACP III planning team to determine appropriate targets to be activated during the project period (2007-2012). We have constructed a dynamical model that captures the mixing patterns between susceptibles and infectives in both low-risk and high-risk groups in the population. Our aim is to project the HIV estimates by taking into account general interventions for susceptibles and additional interventions, such as targeted interventions among high risk groups, provision of anti-retroviral therapy, and behavior change among HIV-positive individuals. Continuing the current level of interventions in NACP II, the model estimates there will be 5.06 million PLHA by the end of 2011. If 50 percent of the targets in NACP III are achieved by the end of the above period then about 0.8 million new infections will be averted in that year. The current status of the epidemic appears to be less severe compared to the trend observed in the late 1990s. The projections based on the second phase and the third phase of the NACP indicate prevention programmes which are directed towards the general and high-risk populations, and HIV-positive individuals will determine the decline or stabilization of the epidemic. Model based results are derived separately for the revised HIV estimates released in 2007. According to revised projections there will be 2.08 million PLHA by 2012 if 50 percent of the targets in NACP III are reached. We perform a Monte Carlo procedure for sensitivity analysis of parameters and model validation. We also predict a positive role of implementation of anti-retroviral therapy treatment of 90 percent of the eligible people in the country. We present methods for obtaining disease progression parameters using convolution approaches. We also extend our models to age-structured populations.
Citation: Arni S. R. Srinivasa Rao, Kurien Thomas, Kurapati Sudhakar, Philip K. Maini. HIV/AIDS epidemic in India and predicting the impact of the national response: Mathematical modeling and analysis. Mathematical Biosciences & Engineering, 2009, 6 (4) : 779-813. doi: 10.3934/mbe.2009.6.779
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