Assessing the impact of vaccination in a COVID-19 compartmental model

BACKGROUND: The aim of this research is to understand the role played by vaccination in the dynamics of a given COVID-19 compartmental model. Most of all, how vaccination modifies the stability, sensitivity, and the reproduction number of a susceptible population. METHODS: The proposed COVID-19 compartmental model (SVEIRD) has seven compartments. Namely, susceptible (S), vaccinated (V), exposed (E, infected but not yet infectious), symptomatic infectious (I(s)), asymptomatic infectious (I(a)), recovered (R), and dead by Covid-19 disease (D). We have developed a computational code to mimic the first wave of the coronavirus pandemic in a state like New York (NYS). FINDINGS: First a stability analysis was carried out. Next, a sensitivity analysis showed that the more relevant parameters are birth rate, transmission coefficient, and vaccine failure. We found an alternative procedure to easily calculate the vaccinated reproductive number of the proposed SVEIRD model. Our graphical results allow to make a comparison between unvaccinated (SEIRD) and vaccinated (SVEIRD) populations. In the peak of the first wave, we estimated 21% (2.5%) and 6% (0.8%) of the unvaccinated (vaccinated) susceptible population was symptomatic and asymptomatic, respectively. At 180 days of the NYS pandemic, the model forecast about 25786 deaths by coronavirus. A vaccine with 95% efficacy could reduce the number of deaths from 25786 to 3784. CONCLUSION: The proposed compartmental model can be used to mimic different possible scenarios of the pandemic not only in NYS, but in any country or region. Further, for an unvaccinated reproductive number R > 1, we showed that the vaccine's efficacy must be greater than the herd immunity to stop the spread of the COVID-19 disease.