Dynamics of Infectious Diseases Incorporating a Testing Compartment

Abstract

In this paper, we construct an infectious disease model with a testing compartment and analyze the existence and stability of its endemic states. We obtain the basic reproduction number, R0, and demonstrate the existence of one endemic equilibrium without testing and one endemic equilibrium with testing and prove their local and global stabilities based on the value of the basic reproduction number, R0. We then apply our model to the US COVID-19 pandemic and find that, for a large parameter set, including those relevant to the SARS-CoV-2 virus, our analytic and numerical results suggest that the trajectories will be trapped to the testing-free state when the testing number is small enough. This indicates that the pandemic may end with a testing-free endemic state through a novel and surprising mechanism called stochastic trapping.