Modeling Infectious Diseases

Throughout this book we have focused entirely on solving ODEs, without delving deeply into their origins or applications. In the present chapter we shift our attention to modeling with ODEs, by exploring a widely studied class of ODE models that describe the spread of infectious diseases. This group of models serves as a good example of how a complex phenomenon can be modeled using relatively simple systems of ODEs. We will derive these models based on a set of fundamental assumptions and discuss the limitations that arise from these assumptions. Although we consider a single application and a single class of models, the fundamental steps of the modeling process are applicable to a wide range of real-world phenomena.