Speaker : Sandra May Abstract: Optimal control on the prevalence of AIDS in the case of Botswana In the last few years, the prevalence of AIDS has dramatically increased in especially African countries. Among these countries, Botswana is of special interest: it has one of the highest prevalence rates worldwide; its one of very few countries trying to provide anti-HIV medication free for those who need it; and there are lots of data concerning the demographic development of the population. In this project, we try to understand how much medication and which proportion of prevention and medication programs are best suited to stem the prevalence of AIDS in Botswana. Therefor we use a validated PDE-model for the population growth in Botswana, which includes several free control functions. These control functions split into different prevention programs and subsidization of medicaments. Our goal is to find their best combination for a given objective. In mathematical terms, this leads to solving a PDE constrained optimization problem. Using the method-of-line we transform the problem into an ODE constrained optimization problem. The resulting formulation is then appropriate to be solved with MUSCOD-II, which implements Bock´s direct multiple shooting method. In the talk, we explain the model and give details of the implementation. Furthermore we show results for a demographic objective (maximum population) and an economic objective (maximum GDP).