In this project I would like to show the students how epidemics (which refers to any phenomena that propagates in a population including infectious diseases, flow of information, spread of wildfires, etc.) are modeled as differential equations and how they run and spread through a group of individuals. We would see how the connectivity and interactions among individuals can speed up or slow down the process and come up with effective strategies to prevent the propagation or to facilitate it. We would look at people as the nodes of the graph and see how the topology of this graph affects the epidemics spread. Given the dynamics of disease propagation models and the arbitrary graphs on which these phenomena occur, we analyze behaviors of the systems and simulate the models. The simulations would be mostly done with Matlab. The code can be provided to the students and they can work with the parameters and learn to interpret what the parameters are and what role they play. The interns will learn about differential equations and what each expression means. They will learn how to model a differential equation in MATLAB and how to run the code. They will have some exposure to graph theory as well. Eventually they will learn about the impact and importance of diffusion processes and how an epidemic can be effectively prevented with vaccination. At the end they will learn how to effectively present what they have learned and have done to an audience.