SIRSi-Vaccine dynamical model for Covid-19 pandemic

TL;DR

This paper introduces the SIRSi-Vaccine model, a comprehensive dynamical system for Covid-19 that incorporates vaccination, asymptomatic cases, and temporary immunity, and applies it to data from major Brazilian cities.

Contribution

The paper presents a novel SIRSi-Vaccine model that integrates vaccination, asymptomatic infections, and temporary immunity, providing a new tool for understanding Covid-19 dynamics.

Findings

Model accounts for unreported cases and temporary immunity.

Conditions for disease-free and endemic equilibria are derived.

Model fitted to data from São Paulo, Santos, and Campinas.

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.