| Immunology, the study of the immune system's response to pathogens, is a diverse and highly complex science. Mathematics provides a means, through the use of models, that assists in the understanding and dissecting of this science. An overview of mathematical models that have been developed for use in studying drug resistant Streptococcus pneumoniae, secondary infections due to the measles virus, and HIV will be presented. The model of secondary infection focuses on the response of macrophages, a cell in the innate immune system, to bacteria and measles. This model provides essential information concerning the interaction between innate immunity and cell mediated immunity, which includes T-cells. This interaction which is responsible for initiating B and T cell responses is important in HIV dynamics. Recently, mathematical modeling has played an important role in the understanding of HIV pathogenesis. I will present the analysis of previous models as well as discuss the development of new models which include delay dynamics, variable drug efficacy, and mutation. These new models have provided new estimates for parameter values crucial in the understanding of HIV dynamics, have highlighted the importance of delays and have supplied more novel insight into the optimal dosing strategy needed to control the emergence of resistant virus. |
