A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public response.

The spread of SARS-CoV-2 in the Canadian province of Ontario has resulted in millions of infections and tens of thousands of deaths to date. Correspondingly, the implementation of modeling to inform public health policies has proven to be exceptionally important. In this work, we expand a previous model of the spread of SARS-CoV-2 in Ontario, "Modeling the impact of a public response on the COVID-19 pandemic in Ontario, " to include the discretized, Caputo fractional derivative in the susceptible compartment. We perform identifiability and sensitivity analysis on both the integer-order and fractional-order SEIRD model and contrast the quality of the fits. We note that both methods produce fits of similar qualitative strength, though the inclusion of the fractional derivative operator quantitatively improves the fits by almost 27% corroborating the appropriateness of fractional operators for the purposes of phenomenological disease forecasting. In contrasting the fit procedures, we note potential simplifications for future study. Finally, we use all four models to provide an estimate of the time-dependent basic reproduction number for the spread of SARS-CoV-2 in Ontario between January 2020 and February 2021.

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

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. © 2022, Wilmington Scientific Publisher. All rights reserved.