Modeling The Impact of Vaccination On COVID-19 And Its Delta Variant

Vaccination is an important means to fight against the spread of the SARS-CoV-2 virus and its variants. In this work, we propose a general susceptible-vaccinated-exposed-infected-hospitalized-removed (SVEIHR) model and derive its basic and effective reproduction numbers. We set Hong Kong as an example to prove the validity of our model. The model shows how the number of confirmed COVID-19 cases in Hong Kong during the second and third waves of the COVID-19 pandemic would have been reduced had vaccination been available then. We then investigate the relationships between various model parameters and the cumulative number of hospitalized COVID-19 cases in Hong Kong for the ancestral and Delta strains of the virus. Next, we compare the evolution of the SVEIHR model to the traditional “herd immunity” threshold where the proportion of vaccinated individuals is static and no further vaccination takes place after model initialization. Numerical results for Hong Kong demonstrate that the static herd immunity threshold corresponds to a cumulative hospitalization ratio of about one percent (assuming the current hospitalization rate of infected individuals is maintained). We also demonstrate that when the vaccination rate is high, the initial proportion of vaccinated individuals can be lowered for while still maintaining the same proportion of cumulative hospitalized individuals.