A Dynamic Reaction-restore-type Transmission-rate Model for COVID-19

COVID-19 became a paradigmatic global pandemic for science, in a real laboratory inserted in reality to understand how some dangerous virus spread can occur in human populations. In this article, a new strategic epidemiological model is proposed, denoted β-SIR. It is because the transmission rate β follows a proper dynamic law, more precisely a reaction-restore type transmission rate model. Some analytical results associated with dynamic consequences are presented for variables of epidemiological interest. It is concluded, observing the geometry of variables plots, such as transmission rate, effective reproductive number, daily new cases, and actives, that pandemic propagation is very sensible to the population behavior, e.g., by adherence to non-pharmaceutical mitigations and loss of compliance levels.