Equilibrium, stability and discretization of some basic epidemic models

Epidemic basic models will be analysed. The goal is to study the stability of equilibrium points using the Lyapunov's indirect method, through the linearisation of the systems to study local stability, and the Lyapunov's direct method to study the global stability of each equilibrium point. A simulation example will show that, despite the simplicity of the models, they can give a good representation of how will be the dynamics of the disease.