Mathematical analysis of a COVID-19 compartmental model with interventions

Mathematical models of the COVID-19 pandemic have been utilized in a variety of settings as a core component of national public health responses. Often based on systems of ordinary differential equations, compartmental models are commonly used to understand and forecast outbreak trajectories. In view of the primarily applied nature of COVID-19 models, theoretical analysis can provide a global and long-term perspective of key model properties, and relevant insights about the infection dynamics they represent. This work formulates and undertakes such an investigation for a compartmental model of COVID-19, which includes the effect of interventions. More specifically, this paper analyzes the characteristics of the solutions of a compartmental model by establishing the existence and stability of the equilibrium points based on the value of the basic reproductive number R0. Our results provide insights on the possible policies that can be implemented to address the health crisis.