1 Epidemic Modeling and Estimation Alberto Abadie 1, 2, 4 Paolo Bertolotti 2, 4 Ben Deaner 1 Arnab Sarker 2, 4 Devavrat Shah 2, 3, 4 1 Department of Economics, MIT 2 Institute for Data, Systems, and Society, MIT 3 Department of EECS, MIT 4 IDSS COVID-19 Collaboration (ISOLAT) Project, IDSS, MIT The purpose of this memo is to summarize various classical and emerging approaches for epidemic modeling. The goal here is to describe the models and the methods for learning such models in a data-driven manner as well as utilizing them for various predictive tasks. 1. Background Overview. Epidemics, such as COVID-19, spread through human interactions. There- fore, at some level, the precise nature and details of human interactions determine how epidemics grow and infection spreads. Epidemiologists have studied this phenomenon and developed remarkably simple, parsimonious models. In addition, at the time of writing this document, the ongoing pandemic of COVID-19 has resulted in various recent proposals to better estimate parameters for existing models, as well as proposals of novel models. We attempt to document such approaches from the biased view of the authors. At their core, epidemiological methods attempt to model the growth of infections and the duration of the epidemic using data. The key information fed into these models involves the number of individuals with infections at any given point of time, the number of individuals recovered from infection, and the number of deaths. In some cases, clinical data may be used. In reality, such observations are noisy: there are delays in reporting, inaccuracies and, most importantly, there is a possibility of lack of detection. Setup. Throughout the document, let t denote time. We shall assume, unless stated otherwise, that the unit of time is days. Let S(t) be fraction (or actual number) of the population that is “susceptible” to receive infection at time t, initially S(0) = 1. Let I (t) denote the fraction (or actual number) of the population that is actively “infected” at time t. Let R(t) denote the fraction (or actual number) of the population that has recovered (or died) at time t. In addition, let E(t) denote the fraction (or actual number) of the population that is “exposed” to infection at time t. Organization. We start by describing deterministic mechanistic models from the epi- demiology literature (see Hethcote 2000, for a recent review). We follow it with statistical models and approaches to learn these mechanistic models from the data. Finally, we end with a recent proposal about a non-mechanistic, non-parametric approach introduced by Sarker & Shah (2020). 2. Deterministic Mechanistic Models The Susceptible-Infectious-Recovered (SIR) model of epidemics was introduced by Ker- mack & McKendrick (1927). Kermack and McKendrick model the flow of individual