Mathematical models for the spread of infectious diseases have a long history. From the start of the Covid-19 pandemic, there was a huge public interest in applying such models, since they help to understand general features of epidemic spread and support the assessment of possible mitigation measures – and their later relaxation. We describe and discuss some well-established mathematical models for epidemic spread, starting from the susceptible-infected-recovered (SIR) model and branching processes and discussing insights from network-based models. During the Covid-19 pandemic, such classical models have also been extended to include many additional aspects that affect epidemic spread, such as mobility patterns or testing possibilities. However, such complex models are increasingly difficult to assess from the outside. In a situation where their predictions can directly affect the lives of millions of people, this can become a severe problem. We argue that simple mathematical models have huge merits and can explain many of the key features of more complex models, such as the importance of heterogeneity in disease transmission. For example, basic models allow inferring whether super-spreading, where very few infected individuals cause the vast majority of secondary cases, should be the rule or the exception – with wide-ranging consequences for the possible success of mitigation measures. In addition, these basic models are simple enough to be understood and implemented without expert knowledge in theoretical epidemiology or computer science. Thus, they offer a level of transparency that can be important for a society to accept mitigation measures
