Abstract
This work presents a new polymorphic, reusable, and comprehensive mathematical model for COVID-19 epidemic transition cycle dynamics. This model has the following characteristics: (1) The core SEIR model includes asymptomatic and symptomatic infections; (2) the symptomatic infection is a multi-variant; (3) the recovery stage provides a partial feed to the symptomatic infection; and (4) the symptomatic and asymptomatic stages have additional feed streams from the protected stage. The proposed formalisation template is a canonical way to achieve different models for the underlying health control environment. This template approach endows the model with polymorphic and reusable capability across different scenarios. To verify the model's reliability and validity, this work utilised two sets of initial conditions: date range and COVID-19 data for Canada and Saudi Arabia.