Linking epidemic models and hawkes point processes for modeling information diffusion

Epidemic models and Hawkes point process models are two common model classes for information diffusion. Recent work has revealed the equivalence between the two for information diffusion modeling. This allows tools created for one class of models to be applied to another. However, epidemic models and Hawkes point processes can be connected in more ways. This thesis aims to develop a rich set of mathematical equivalences and extensions, and use them to ask and answer questions in social media and beyond. Specifically, we show our plan of generalizing the equivalence of the two model classes by extending it to Hawkes point process models with arbitrary memory kernels. We then outline a rich set of quantities describing diffusion, including diffusion size and extinction probability, introduced in the fields where the models are originally designed. Lastly, we discuss some novel applications of these quantities in a range of problems such as popularity prediction and popularity intervention.