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In this talk we discuss the link between real world systems and the development of appropriate model equations. Our focus is on problems that involve a history, delay or after-effect, and we begin with a discussion of how these phenomena can be reflected in relatively simple model equations. We discuss approaches to model selection and parameter estimation. We give examples that show how different modelling paradigms can be necessary to develop effective models in different circumstances.
We go on to consider examples of well-intentioned approaches to the construction of models which contain fundamental errors, and we see how these errors can show up in approximate solutions and simulations. We give examples that show why the conclusions drawn from the model may be quite unhelpful to the application and we provide some ideas about how to avoid these problems arising. If time permits we shall consider relevant lessons from modelling of the recent COVID-19 pandemic.
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