Compartmental model with loss of immunity: analysis and parameters estimation for Covid-19

TL;DR

This paper introduces a modified SIRSi compartmental model for Covid-19 that accounts for varying immunity and asymptomatic cases, and applies it to three cities in São Paulo to estimate outbreak dynamics.

Contribution

It proposes a novel SIRSi model incorporating immunity loss and unreported cases, with parameter estimation for specific cities.

Findings

Model fits well to city data

Estimated outbreak peaks and durations

Highlights importance of immunity loss in Covid-19 dynamics

Abstract

The outbreak of Covid-19 led the world to an unprecedent health and economical crisis. In an attempt to responde to this emergency researchers worldwide are intensively studying the Covid-19 pandemic dynamics. In this work, a SIRSi compartmental model is proposed, which is a modification of the known classical SIR model. The proposed SIRSi model considers differences in the immunization within a population, and the possibility of unreported or asymptomatic cases. The model is adjusted to three major cities of S\~ao Paulo State, in Brazil, namely, S\~ao Paulo, Santos and Campinas, providing estimates on the duration and peaks of the outbreak.