Dynamics of Functional Differential Equations with Applications in Epidemiology

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Models of the spread of infectious disease can be expressed in many ways, including as ordinary differential equations (ODEs) or as functional differential equations (FDEs). Examples of FDEs include delay differential equations (DDEs) and partial differential equations (PDEs). Often FDE models are direct generalizations of simpler ODE models, including additional features that may be related to the history of the system. The analysis of FDEs has been developed over the last 50 years, but is still much more complicated than the analysis of ODEs.