Mathematical modelling of AIDS epidemic in India

Mathematical and statistical models can serve as tools for understanding the epidemiology of human immunodeficiency virus and acquired immunodeficiency syndrome if they are constructed carefully. This article is meant to be an introduction to AIDS-related mathematical biology for scientists with a non-mathematical background. An applicable dynamical model is also explained

"U" Type Functions

A function from the exponential family is proved to have U shape in certian interval. When one of the coefficients is negative then the functional form will be the exact mirror image of its original function. Volume of such U shaped vessel is calcluated

Limiting Theorems on 'Case' Reporting

The relation between reported disease cases and actual cases(hypothetical) is defined. Certain situations where such sequences of relation converge or diverge is studied

Probabilities of Therapeutic Extinction of HIV

Using branching process principles and recent developments in HIV immunology, a methodology is demonstrated to compute the probability of extinction of HIV in the presence of protease inhibitors

Can we obtain realistic HIV/AIDS estimates for India ?

Recent reports have indicated that China, India and Russia are headed for a major public health calamity with regard to AIDS if indeed the calamity is not already upon these countries. It is therefore of some concern that there is uncertainty associated with existing estimates of the number of HIV infected individuals in India. According to a report, the US Central Intelligence Agency has predicted that India will have 25 million AIDS cases by 2010 (National Intelligence Council, USA 2002). The Government of India was quick to point out that these estimates are exaggerated. The World Bank has projected 10.9 million AIDS cases by 2024 (The Hindu, 17 November 2002), on the assumption that adequate intervention measures are implemented (table 1). The National AIDS Control Organisation (NACO) (2002), the nodal agency for HIV surveillance in India has estimated 3.97 million HIV cases by the end of year 2001. In this article, I try to highlight the importance of accuracy of HIV estimates. I assume that infection by HIV in an individual is a strong indicator of the future development of AIDS

A combination of differential equations and convolution in understanding the spread of an epidemic

Nonlinear dynamical method of projecting the transmission of an epidemic is accurate if the input parameters and initial value variables are reliable. Here, such a model is proposed for predicting an epidemic.A method to supplement two variables and two parameters for this proposed model is demonstrated through a robust statistical approach. The method described here worked well in case of three continuous distributions. Model predictions could be lower estimates due to under-reporting of disease cases. An ad hoc procedure with a technical note is provided in the appendix

Incubation-Time Distribution in Back-Calculation Applied to HIV/AIDS Data in India

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 the deconvolution technique and the 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 the 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

Parametric models for incubation distribution in presence of left and right censoring

When both left and right censoring are present in the data simultaneously, estimating the incubation distribution becomes difficult. In this paper we have introduced several parametric models and have estimated the parameters by the method of moments. A numerical study explores the efficacy of the method