Mathematical modelling of HIV-1 dynamics in vivo

The increasing attention in the scientific world towards a quantitative approach to the biological sciences has produced useful and interesting work, giving rise to Biomathematics as a well defined discipline. For applications in some fields of medicine and biology, we also have a theory and a specific formalism [1, 2]. However, in some areas, given the complexity of the studied systems and the difficulty of finding detailed informations, there is no accepted basis for modeling. This is the case for the HIV infection that we are considering in this thesis. Since we model a complex biological system, in Chapter 1 a brief, but somewhat detailed description is given. We chose to put it at the beginning because we believe that modeling in Biomathematics should always be biologically correct and the extent of approximations should be clear. From this point of view, the models we present in Chapters 3 and 4 represent an effort of synthesis of these two guidelines. An important part of the job has been to get out of the description a bio-mathematical model. In this context, the researcher in Biomathematics needs to master concepts and language of biology and to get continuous exchange with biological researchers. Moreover, we are well convinced that the bio-mathematical model must be constructed starting from a well defined biological question. There are some examples in Chapter 2. The main objectives of this thesis are to investigate the basic and most important cause-effect relations of the phenomenon, as we do in Chapter 3, and to estimate biological parameters difficult to measure, starting from the features of the model and its solutions, as is presented in Chapter 4.