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. 2021 Nov 2;54(15):151–156. doi: 10.1016/j.ifacol.2021.10.247

Vaccination and social distance to prevent COVID-19⁎

Cristiane M Batistela ⁎, Marien M Ramos ⁎⁎, Manuel AM Cabrera ⁎⁎⁎, Giovanni M Dieguez ⁎⁎⁎⁎, José RC Piqueira †
PMCID: PMC8562104  PMID: 38620952

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 Rv to validate the theoretical results.

Keywords: SIR model, social distancing, stability, vaccination, reproduction number

Footnotes

⁎

Marien M. Ramos is supported by FDTE/CAPES-Brazil; Manuel A.M. Cabrera is supported by CAPES-Brazil; Jose R.C. Piqueira is supported by CNPq.

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