STRUCTURAL AND PRACTICAL IDENTIFIABILITY ANALYSES ON THE TRANSMISSION DYNAMICS OF COVID-19 IN THE UNITED STATES

Abstract

We formulate an epidemic model to capture essential epidemiology of COVID-19 and major public health interventions. We start with a system of differential equations involving six compartments, and we use the Goodman and Weare affine invariant ensemble Markov Chain Monte Carlo algorithm (GWMCMC) to identify a simplified version of the full model that consists of only four compartments. We examine well-posedness of the relevant parameter estimation problem for the given observations using the U.S. epidemic data; study the reliability of model selection; analyze the structural identifiability of the selected model; and conduct a practical identifiability analysis on the selected model using the GWMCMC algorithm. Our study shows that the selected model is structurally identifiable for the confirmed cases, and for small measurement errors, key parameters such as the transmission rate are practically identifiable. We also analyze the stability of the selected model and prove the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium by constructing appropriate Lyapunov functions. Our numerical experiments show that the U.S. will undergo damped transit oscillations towards the endemicity.