The importance of mathematical models able to predict the dynamic behaviour of an infectious disease has been consolidated in the last year. In this thesis, we examine the SIR compartmental model, both in the scalar and network case, to account for endogenous individuals behaviours and population heterogeneities. In the first part, after an initial simulation of the classic behaviour, there is a presentation of several modified versions of the model, in which a mitigation term for social interactions is included. This addition, expressed as a function of the fraction of infected, can express either an individual reaction to the presence of the disease or a governments measures, imposed to limit interactions and contain contagion.