Computing the COVID-19 Basic and Effective Reproduction Numbers Using Actual Data: SEIRS Model with Vaccination and Hospitalization

A novel time-dependent deterministic SEIRS model, extended with vaccination, hospitalization, and vital dynamics, is introduced. Time-varying basic and effective reproduction numbers associated with this model are defined, which are crucial metrics in understanding epidemic dynamics. Furthermore, a parameter identification approach has been used to develop a numerical method to compute these numbers for long-term epidemics. We analyze the actual COVID-19 data from the USA, Italy, and Bulgaria to solve appropriate inverse problems and gain an understanding of the time evolution behavior of the basic and effective reproduction numbers. Moreover, an insightful comparison of key coronavirus data and epidemiological parameters across these countries has been conducted. For this purpose, while the basic and effective reproduction numbers provide insights into the virus transmission potential, we propose data-driven criteria for assessing the actual realization of the transmission potential of the SARS-CoV-2 virus and the effectiveness of the applied restrictive measures. To obtain these results, we conduct a mathematical analysis to demonstrate various biological properties of the new differential model, including non-negativity, boundedness, existence, and uniqueness of the solution. The new model and the associated numerical simulation tools proposed herein could be applied to COVID-19 data in any country worldwide and hold a promising potential for the transmission capacity and impact of the virus.