A Vaccination-Socialization SIR Model for Covid-19: Lessons Learned from the Pandemic
Denver F. Cheddie *
Utilities and Sustainable Engineering, University of Trinidad and Tobago, Point Lisas Campus, 91-101 Esperanza Road, Brechin Castle, California -540517, Trinidad and Tobago.
*Author to whom correspondence should be addressed.
Abstract
Background: Modified SIR models have been effective in simulating the spread of Covid-19 and predicting various phenomena associated with the pandemic.
Aims: This paper presents a vaccination-socialization model to determine the relative effects of vaccination and increased socialization among the vaccinated. The objective is to determine whether the disease is spread more so by the presence of the unvaccinated or by increased social activity among the vaccinated.
Methodology: To accomplish this, the SIR model is modified to include 9 compartments and 3 sub-populations. The resulting system of differential equations is solved in Matlab’s programming language using the 4th order Runge-Kutta method.
Results: The results show that the concept of a safe-zone in which vaccinated persons can increase their social activity only applies if the vaccine effectiveness is very high.
Keywords: Covid-19, SIR model, compartmental model, vaccination, herd immunity