A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations

The novel coronavirus (COVID-19) pandemic that emerged from Wuhan city in December 2019 overwhelmed health systems and paralyzed economies around the world. It became the most important public health challenge facing mankind since the 1918 Spanish flu pandemic. Various theoretical and empirical approaches have been designed and used to gain insight into the transmission dynamics and control of the pandemic. This study presents a primer for formulating, analysing and simulating mathematical models for understanding the dynamics of COVID-19. Specifically, we introduce simple compartmental, Kermack-McKendrick-type epidemic models with homogeneously- and heterogeneously-mixed populations, an endemic model for assessing the potential population-level impact of a hypothetical COVID-19 vaccine. We illustrate how some basic non-pharmaceutical interventions against COVID-19 can be incorporated into the epidemic model. A brief overview of other kinds of models that have been used to study the dynamics of COVID-19, such as agent-based, network and statistical models, is also presented. Possible extensions of the basic model, as well as open challenges associated with the formulation and theoretical analysis of models for COVID-19 dynamics, are suggested.