Modeling the COVID-19 pandemic: A primer and overview of mathematical epidemiology

TL;DR

This paper reviews fundamental and advanced mathematical models used to understand and predict various aspects of the COVID-19 pandemic, including transmission dynamics, interventions, and viral evolution.

Contribution

It provides a comprehensive overview of the mathematical modeling approaches, their extensions, and their applications to COVID-19, highlighting key findings and limitations.

Findings

Heterogeneity affects disease transmission dynamics

Non-pharmaceutical interventions impact pandemic control

Models reveal potential for vaccine escape and viral evolution

Abstract

Since the start of the still ongoing COVID-19 pandemic, there have been many modeling efforts to assess several issues of importance to public health. In this work, we review the theory behind some important mathematical models that have been used to answer questions raised by the development of the pandemic. We start revisiting the basic properties of simple Kermack-McKendrick type models. Then, we discuss extensions of such models and important epidemiological quantities applied to investigate the role of heterogeneity in disease transmission e.g. mixing functions and superspreading events, the impact of non-pharmaceutical interventions in the control of the pandemic, vaccine deployment, herd-immunity, viral evolution and the possibility of vaccine escape. From the perspective of mathematical epidemiology, we highlight the important properties, findings, and, of course, deficiencies, that all these models have.