Mathematical assessment of the role of waning and boosting immunity against the BA.1 Omicron variant in the United States
Authors: Safdar Salman , Ngonghala Calistus N. , Gumel Abba B. 
Published: July 2022

Three safe and effective vaccines against SARS-CoV-2 (the Pfizer-BioNTech, Moderna and Johnson & Johnson vaccines) have played a major role in combating the COVID-19 pandemic in the United States. However, the effectiveness of these vaccines and vaccination programs has been challenged by the emergence of new SARS-CoV-2 variants of concern. A new mathematical model is formulated to assess the population-level impact of the waning and boosting of vaccine-derived and natural immunity against the Omicron variant in the United States. To account for gradual waning of vaccine-derived immunity, we considered three vaccination classes (V1, V2 and V3; where subscripts 1, 2 and 3 represent high, moderate and low levels of immunity, respectively). The disease-free equilibrium of the model was shown to be globally-asymptotically stable, for two special cases, whenever a certain associated epidemiological quantity, known as the vaccination reproduction number of the model, is less than one. The model was fitted using observed daily case data for the Omicron BA.1 variant in the United States. Simulations of the resulting parameterized model showed that, for the case where the high-level of the vaccine-derived protective efficacy received by individuals in the first vaccinated class (V1) is set at its baseline value (85%; while the vaccine-protective efficacy for individuals in the V2 and V3 classes, as well as natural immunity, are maintained at baseline), population-level herd immunity can be achieved in the United States via vaccination-boosting strategy, if at least 59% of the susceptible populace is fully-vaccinated followed by the boosting of about 71.5% of the fully-vaccinated individuals whose vaccine-derived immunity has waned to moderate or low level. However, if the high level of vaccine-induced efficacy for individuals in the V1 class is reduced to 55%, for instance, achieving herd immunity requires fully-vaccinating at least 91% of the susceptible population (followed by marginal boosting of those in whom the vaccine-derived immunity has waned to moderate or low level). In the absence of boosting of vaccine-derived and natural immunity, waning of immunity (both vaccine-derived and natural) only causes a marginal increase in the average number of new cases at the peak of the pandemic. Boosting of both immunity types at baseline could result in a dramatic reduction in the average number of daily new cases at the peak, in comparison to the corresponding waning scenario without boosting of immunity. Furthermore, boosting of vaccine-derived immunity (at baseline) is more beneficial (in reducing the burden of the pandemic) than boosting of natural immunity (at baseline). Specifically, for the fast waning of immunity scenario (where both vaccine-derived and natural immunity are assumed to wane within three months), boosting vaccine-derived immunity at baseline reduces the average number of daily cases at the peak by 90% (in comparison to the corresponding scenario without boosting of the vaccine-derived immunity), whereas boosting of natural immunity (at baseline) only reduced the corresponding peak daily cases (in comparison to the corresponding scenario without boosting of natural immunity) by 62%. It was further shown that boosting of vaccine-derived (implemented near the baseline level) increased the prospects of altering the trajectory of COVID-19 from persistence to possible elimination (even for the fast waning scenario of vaccine-derived immunity). Thus, a vaccination strategy that emphasizes boosting of immunity would significantly enhance the prospects of SARS-CoV-2 elimination in the United States.