Abstract:
This dissertation is primarily concerned with dynamic HIV/AIDS parameter estimation, set against the background of engineering, biology and medical science. The marriage of these seemingly divergent fields creates a dynamic research environment that is the source of many novel results and practical applications for people living with HIV/AIDS. A method is presented to extract model parameters for the three-dimensional HIV/AIDS model in situations where an orthodox LSQ method would fail. This method allows information from outside the dataset to be added to the cost functional so that parameters can be estimated even from sparse data. Estimates in literature were for at most two parameters per dataset, whereas the procedures described herein can estimate all six parameters. A standard table for data acquisition in hospitals and clinics is analyzed to show that the table would contain enough information to extract a suitable parameter estimate for the model. Comparison with a published experiment validates the method, and shows that it becomes increasingly hard to coordinate assumptions and implicit information when analyzing real data. Parameter variations during the course of HIV/AIDS are not well understood. The results show that parameters vary over time. The analysis of parameter variation is augmented with a novel two-stage approach of model identification for the six-dimensional model. In this context, the higher-dimensional models allow an explanation for the onset of AIDS from HIV without any variation in the model parameters. The developed estimation procedure was successfully used to analyze the data from forty four patients of Southern Africa in the HIVNET 28 vaccine readiness trial. The results are important to form a benchmark for the study of vaccination. The results show that after approximately 17 months from seroconversion, oscillations in viremia flattened to a log10 based median set point of 4:08, appearing no different from reported studies in subtype B HIV-1 infected male cohorts. Together with these main outcomes, an analysis of confidence intervals for set point, days to set point and the individual parameters is presented. When estimates for the HIVNET 28 cohort are combined, the data allows a meaningful first estimate of parameters of the three-dimensional HIV/AIDS model for patients from southern Africa. The theoretical basis is used to develop an application that allows medical practitioners to estimate the three-dimensional model parameters for HIV/AIDS patients. The program demands little background knowledge from the user, but for practitioners with experience in mathematical modeling, there is ample opportunity to fine-tune the procedures for special needs.
