Modified SIQR model for the COVID-19 outbreak in several countries

In this paper, we propose a modified Susceptible-Infected-Quarantine-Recovered (mSIQR) model, for the COVID-19 pandemic. We start by proving the well-posedness of the model and then compute its reproduction number and the corresponding sensitivity indices. We discuss the values of these indices for epidemiological relevant parameters, namely, the contact rate, the proportion of unknown infectious, and the recovering rate. The mSIQR model is simulated, and the outputs are fit to COVID-19 pandemic data from several countries, including France, US, UK, and Portugal. We discuss the epidemiological relevance of the results and provide insights on future patterns, subjected to health policies.