Mathematical analysis of a two-strain compartmental model with vaccination and quarantine

We formulate a two-strain compartmental model that incorporates interventions such as vaccination and quarantine. The model is applicable for infectious diseases such as Influenza and COVID-19, and it’s expressed as a system of ordinary differential equations. We establish the existence of four equilibrium solutions based on reproduction numbers R0,1 and R0,2, and threshold parameters R˜1 and R˜2. The local and global stability of each of these solutions is then analyzed, providing a long term outlook on epidemic progression. Numerical simulations that support the results on stability are also presented.