SIRSi-Vaccine dynamical model for Covid-19 pandemic

Abstract: The Severe Acute Respiratory Syndrome Corona Virus 2 (SARS-CoV-2), or Covid-19, burst into a pandemic in the beginning of 2020. An unprecedented worldwide effort involving academic institutions, regulatory agencies and industry is facing the challenges imposed by the rapidly spreading disease. Emergency use authorization for vaccines were granted in the beginning of December 2020 in Europe and nine days later in the United States. The urge for vaccination started a race, forcing governs and health care agencies to take decisions on the fly regarding the vaccination strategy and logistics. So far, the vaccination strategies and non-pharmaceutical interventions, such as social distancing and the use of face masks, are the only efficient actions to stop the pandemic. In this context, it is of fundamental importance to understand the dynamical behavior of the Covid-19 spread along with possible vaccination strategies. In this work a Susceptible - Infected - Removed - Sick with vaccination (SIRSi-Vaccine) model is proposed. In addtion, the SIRSi-Vaccine model also accounts for unreported, or asymptomatic, cases and the possibility of temporary immunity, either after infection or vaccination. Disease free and endemic equilibrium points existence conditions are determined in the (! ? ?) vaccine-effort and social distancing parameter space. The model is adjusted to the data from S~ao Paulo, Santos and Campinas, three major cities in the State of S~ao Paulo, Brazil.