Vaccination and social distance to prevent COVID-19

Cristiane M Batistela; Marien M Ramos; Manuel A M Cabrera; Giovanni M Dieguez; José R C Piqueira

doi:10.1016/j.ifacol.2021.10.247

Vaccination and social distance to prevent COVID-19

IFAC Pap OnLine. 2021;54(15):151-156. doi: 10.1016/j.ifacol.2021.10.247. Epub 2021 Nov 2.

Authors

Cristiane M Batistela¹, Marien M Ramos¹, Manuel A M Cabrera¹, Giovanni M Dieguez², José R C Piqueira¹

Affiliations

¹ Control Engineering Department, São Paulo University, São Paulo, Brazil.
² Control Engineering Department, São Paulo University, São Paulo.

Abstract

In order to analyze the effect of vaccination in a population with the presence of viruses, a variation of the SIR (Susceptible-Infected-Removed) model is proposed taking into account social distancing and the effect of the vaccine. The equilibrium points of the proposed model are calculated and the stability analysis of the system is carried out. For the proposed model, disease-free equilibrium point and endemic equilibrium point are found and the conditions of existence are discussed. For the disease-free equilibrium point the bifurcation conditions are derived and simulations show that reducing the vaccination effort can lead the disease-free equilibrium to the endemic equilibrium. From the theoretical analysis, a minimum value of effort is obtained to guarantee a disease-free equilibrium point. Simulations were carried out from the value obtained from R_v to validate the theoretical results.

Keywords: SIR model; reproduction number; social distancing; stability; vaccination.