This MQP can be divided into three main chapters. For each chapter, we studied three different mathematical models, which are the Logistic Growth model, the SIR model and the Chemostat model. These biological mathematical models all have time delay in part of their processes. Based on the specific phenomenological assumptions, we have different ways of building up the model through ordinary differential equations. The goal of this project is to investigate three models with time delay. We will also perform global sensitivity analysis for each model and study how uncertainty in the output of each model can be attributed to different sources of uncertainty in the model input. Applications for each model with time delay will be provided in this project with numerical results.