SIRSi compartmental model for COVID-19 pandemic with immunity loss

• Published in: Chaos, solitons and fractals solitons and fractals, 2021-01, Vol.142, p.110388-110388, Article 110388
• Main Authors: Batistela, Cristiane M., Correa, Diego P.F., Bueno, Átila M, Piqueira, José Roberto C.
• Format: Article
• Language: English
• Subjects: Compartmental models; Covid-19; Equilibrium analysis; Parameter fitting
• ISSN: 0960-0779; 1873-2887; 0960-0779
• DOI: 10.1016/j.chaos.2020.110388

•A modification of SIR model, SIRSi model, was fitted to data of the Covid-19 outbreak.•The model is able to estimate the duration and peaks of the outbreak.•Additionally, the model allows to infer unreported and asymptomatic cases.•The model contains a feedback loop considering different immunity responses. The coronavirus disease 2019 (Covid-19) outbreak led the world to an unprecedented health and economic crisis. In an attempt to respond to this emergency, researchers worldwide are intensively studying the dynamics of the Covid-19 pandemic. In this study, a Susceptible - Infected - Removed - Sick (SIRSi) compartmental model is proposed, which is a modification of the classical Susceptible - Infected - Removed (SIR) model. The proposed model considers the possibility of unreported or asymptomatic cases, and differences in the immunity within a population, i.e., the possibility that the acquired immunity may be temporary, which occurs when adopting one of the parameters (γ) other than zero. Local asymptotic stability and endemic equilibrium conditions are proved for the proposed model. The model is adjusted to the data from three major cities of the state of São Paulo in Brazil, namely, São Paulo, Santos, and Campinas, providing estimations of duration and peaks related to the disease propagation. This study reveals that temporary immunity favors a second wave of infection and it depends on the time interval for a recovered person to be susceptible again. It also indicates the possibility that a greater number of patients would get infected with decreased time for reinfection.