The general objective of this work is to deal with different approaches for the representation of an epidemic considering the state of the individuals in the population, Susceptible, Infected or Recovered (SIR), which generate models that students can explore with the computer using the contents acquired in mathematics subjects. Specifically, the purposes of the tasks designed focus on the identification and analyses of the variables and parameters involved in an epidemic through three modelling methodologies: i) Simple systems of ordinary differential equations reflecting the SIR representation; ii) Systems of difference equations and matrix representations by means of discretization of the time variable in the SIR formulation; and iii) Computational simulations from the use of the agent-based model “Virus” already implemented in the NetLogo platform. Exploration and comparison of the dynamics of Ebola and AIDS epidemics show the students the potential of modelling in this context and allow them to link with real applications. The assessment given by students of this activity was positive showing their interest in the topic