We consider a biologically based mathematical model (system of ODEs) that describe a disease prevalence in a logistically growing population. Some vaccine parameters in both childhood and adult stages are considered in the model to control the disease. Then we introduce some optimization problems constrained by this system of ODEs. We use optimal problems to find vaccine optimal parameters that imply the most cost-effective method for introducing vaccine for this population. The optimal problem is implemented and solved using MATLAB coding. This work will help in improving the way of delivering vaccine at schools and health units in the UAE, and will also help policy making in controlling any possible future health problems. This research project target a worldwide health problem and will support the research activity in both the Mathematics Department and the College of Medicine and Health Sciences at Khalifa University.