Theory of Infectious Diseases with Testing and Testing-less Covid-19 Endemic

What is the long term dynamics of the Covid-19 pandemic? How will it end? Here we constructed an infectious disease model with testing and analyzed the existence and stability of its endemic states. For a large parameter set, including those relevant to the SARS-CoV-2 virus, we demonstrated the existence of one endemic equilibrium without testing and one endemic equilibrium with testing and proved their local and global stabilities for some cases. Our results suggest that the pandemic is to end with a testing-less endemic state through a novel and surprising mechanism called stochastic trapping.