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A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations
Abba B Gumel1,2, Enahoro A Iboi3, Calistus N Ngonghala4,5
1School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, 85287, USA.
Infectious Disease Modelling
|January 21, 2021
Summary
This study provides a guide to mathematical modeling for understanding COVID-19 transmission dynamics. It introduces compartmental models and discusses interventions, offering insights into pandemic control strategies.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health
Background:
- The COVID-19 pandemic posed unprecedented global health and economic challenges.
- Understanding transmission dynamics is crucial for effective pandemic control.
- Mathematical modeling offers a powerful framework for analyzing epidemic spread.
Purpose of the Study:
- To present a primer on formulating, analyzing, and simulating mathematical models for COVID-19 dynamics.
- To introduce compartmental epidemic models, including Kermack-McKendrick-type models.
- To explore the incorporation of non-pharmaceutical interventions and vaccine impact into models.
Main Methods:
- Development of simple compartmental models for homogeneously and heterogeneously mixed populations.
- Introduction of an endemic model to assess vaccine impact.
- Illustration of how non-pharmaceutical interventions can be integrated into epidemic models.
- Overview of agent-based, network, and statistical models used for COVID-19.
Main Results:
- The study provides a foundational understanding of mathematical modeling approaches for COVID-19.
- It demonstrates the utility of compartmental models in simulating disease spread and intervention effects.
- The research highlights the flexibility of these models for incorporating various epidemiological factors.
Conclusions:
- Mathematical models are essential tools for understanding and managing infectious disease outbreaks like COVID-19.
- The presented primer facilitates the application of these models for research and policy-making.
- Further research is needed to address open challenges in COVID-19 modeling and its extensions.
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