A mathematical model of COVID-19 with a delay-term for the vaccinated compartment is developed. It has parameters accounting for vaccine-induced immunity delay, vaccine effectiveness, vaccination rate, and vaccine-induced immunity duration. The model parameters before vaccination are calibrated with the Philippines’ confirmed cases. Simulations show that vaccination has a significant effect in reducing future infections, with the vaccination rate being the dominant determining factor of the level of reduction. Moreover, depending on the vaccination rate and the vaccine-induced immunity duration, the system could reach a disease-free state but could not attain herd immunity. Simulations are also done to compare the effects of the various available vaccines. Results show that Pfizer-BioNTech has the most promising effect while Sinovac has the worst result relative to the others.

Coronavirus disease 2019 (COVID-19) management and response is a challenging task due to the uncertainty and complexity of the nature surrounding the virus. In particular, the emergence of new variants and the polarizing response from the populace complicate government efforts to control the pandemic. In this study, we developed a compartmental model that includes (1) a vaccinated compartment, (2) reinfection after a particular time, and (3) COVID-19 variants dominant in the Philippines. Furthermore, we incorporated stochastic terms to capture uncertainty brought about by the further evolution of the new variants and changing control measures via parametric perturbation. Results show the importance of booster shots that increase the vaccine-induced immunity duration. Without booster shots, simulations showed that the dominant strain would still cause significant infection until 31 December 2023. Moreover, our stochastic model output showed significant variability in this case, implying greater uncertainty with future predictions. All these adverse effects, fortunately, can be effectively countered by increasing the vaccine-induced immunity duration that can be done through booster shots.