Numerical simulation shows vaccines’ impact on COVID-19 control: a cautionary tale for spread and control

Abstract

The purpose of this study was to use a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model to forecast the dynamics of the COVID-19 epidemic in the high and low pandemic cases that occurred in the State of Paraná, Brazil in 2021. Subsequently, the findings of this analysis were compared. The model parameters were adjusted based on official reports from the State of Paraná, Brazil. As a result, it can be observed that the parameters for susceptible population (S) and exposed population (E) tend to decay over time, with a more drastic drop for S and a slower decrease for E in high pandemics. Conversely, the parameter for infected population (I) tends to rise and decay over time, with a tendency to grow in high pandemics. Additionally, the parameter for recovered population (R) tends to rise over time, with a much higher growth rate in low pandemics than in high pandemics, as expected. The numerical simulation appears to align with reality, which is consistent with the scenario in various cities worldwide. Additionally, the implemented model has several advantages, including accurate adjustments despite the simplicity of the hypotheses and projections that are comparable to those of more complex models. The findings presented may provide useful suggestions for the prevention and management of COVID-19 outbreaks in different countries and regions.