Relevant mathematical modelling efforts for understanding COVID-19 dynamics: an educational challenge

The purpose of the work described in this paper is to emphasize the importance of using mathematical models and mathematical modelling in order to be able to understand and to learn possible behaviours in epidemic situations such as that of the COVID-19 pandemic, besides suggesting modelling techniques with which to evaluate certain sanitary decisions and policies which do, in fact, affect society as a whole. The mathematical tools that are used derive from nonlinear systems of difference equations (possibly viable at a high school level, using spreadsheets or adequate software) as well as nonlinear systems of ordinary differential equations (therefore using mathematical tools and software well within the reach of undergraduate students of many courses). This purpose is accomplished by motivating students and learners to study existing SIR-type models and modifying them in order to have a fully understandable translation of dynamics for infectious diseases such as COVID-19 in several different realistic scenarios, that is to say, situations that consider social distancing policies, widespread vaccination programmes, as well as possible and even probable results when in the presence of negationist postures and attitudes. Several modelling choices referring to real-life situations are shown and explored. These models are analysed and discussed, implicitly proposing similar attitudes and evaluations in learning environments. Conclusions are drawn, stimulating further work using the described mathematical tools and resources.