This study is a primer for formulating, analyzing and simulating mathematical models for understanding the dynamics of COVID-19, the novel corona virus that emerged from Wuhan city in December 2019. A basic modeling framework, based on using a simple compartmental deterministic epidemic modeling a homogeneous population, is illustrated for gaining insight into the transmission dynamics of COVID-19 which is also developed to stochastic case. This simple model can be extended to include the population-level impact of a COVID-19 vaccine.