  The COronaVIrus Disease 2019 (COVID-19) pandemic that has had the world in
its grip from the beginning of 2020, has resulted in an unprecedented level of
public interest and media attention on the field of mathematical epidemiology.
Ever since the disease came to worldwide attention, numerous models with
varying levels of sophistication have been proposed; many of these have tried
to predict the course of the disease over different time-scales. Other models
have examined the efficacy of various policy measures that have been adopted
(including the unparalleled use of "lockdowns") to contain and combat the
disease. This multiplicity of models may have led to bewilderment in many
quarters about the true capabilities and utility of mathematical modeling. Here
we provide a brief guide to epidemiological modeling, focusing on how it has
emerged as a tool for informed public-health policy-making and has in turn,
influenced the design of interventions aimed at preventing disease outbreaks
from turning into raging epidemics. We show that the diversity of models is
somewhat illusory, as the bulk of them are rooted in the compartmental modeling
framework that we describe here. While their basic structure may appear to be a
highly idealized description of the processes at work, we show that features
that provide more realism, such as the community organization of populations or
strategic decision-making by individuals, can be incorporated into such models.
We conclude with the argument that the true value of models lies in their
ability to test in silico the consequences of different policy choices in the
course of an epidemic, a much superior alternative to trial-and-error
approaches that are highly costly in terms of both lives and socio-economic
disruption.
