Vortrag im Rahmen des Kolloquium Nonlinear Science Dengue is a viral disease principally transmitted by Aedes aegypti mosquitoes. There is no vaccine to protect against dengue; therefore, dengue morbidity can only be reduced by appropriate vector control measures, such as: - suppression of the mosquito population, - reduction of the disease transmissibility. This presentation will be focused on implementation of these external control actions using the frameworks of mathematical modeling and control theory approach. In the first part, I will present and endemo-epidemic model derived from registered dengue case in Cali, Colombia and then propose a set of optimal strategies for dengue prevention and control. In the second part, I will present an alternative and unconventional vector control technique based on the use of biological control agent (Wolbachia) and formulate a decision-making model for Wolbachia transinfection in wild Aedes aegypti populations.