A model for the outbreak of COVID-19: Vaccine effectiveness in a case study of Italy

TL;DR

This paper introduces a compartmental mathematical model for COVID-19 spread in Italy, analyzing vaccine effectiveness and stability, providing insights into infection control with imperfect vaccines.

Contribution

It develops a new model incorporating asymptomatic cases and demography, and derives threshold conditions for vaccination strategies to prevent outbreaks.

Findings

Basic reproductive ratio computed for Italy

Stability analysis of the disease-free equilibrium

Threshold conditions for vaccination effectiveness

Abstract

We present a compartmental mathematical model with demography for the spread of the COVID-19 disease, considering also asymptomatic infectious individuals. We compute the basic reproductive ratio of the model and study the local and global stability for it. We solve the model numerically based on the case of Italy. We propose a vaccination model and we derive threshold conditions for preventing infection spread in the case of imperfect vaccines.