Abstract
Abstract 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.
Highlights
The COVID-19 pandemic, which was reported to have originated from China [18], is a rapidly evolving public health problem that immobilized nearly the entire world, causing many social disruptions, and brought havoc on many nations’ economies
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 e ectiveness, vaccination rate, and vaccine-induced immunity duration
In [1], Acuña-Zegarra et al formulated an optimal control problem with mixed constraints to study optimal vaccination policies. Their solution identi es vaccination policies that minimize the burden of COVID-19 quanti ed by the number of disability-adjusted years of life lost
Summary
Randy L. Caga-anan*, Michelle N. Raza, Grace Shelda G. Labrador, Ephrime B. Metillo, Pierre del Castillo, and Youcef Mammeri E ect of Vaccination to COVID-19 Disease Progression and Herd Immunity https://doi.org/10.1515/cmb-2020-0127 Received July 17, 2021; accepted December 3, 2021
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