Abstract:
Multiple effective vaccines are currently being deployed to combat the COVID-19
pandemic, and are viewed as the major factor in marked reductions of disease burden
in regions with moderate to high vaccination coverage. The effectiveness of COVID-19
vaccination programs is, however, significantly threatened by the emergence of new
SARS-COV-2 variants that, in addition to being more transmissible than the wild-type
(original) strain, may at least partially evade existing vaccines. A two-strain (one wildtype,
one variant) and two-group (vaccinated or otherwise) mechanistic mathematical
model is designed and used to assess the impact of the vaccine-induced cross-protective
efficacy on the spread the COVID-19 pandemic in the United States. Rigorous analysis of
the model shows that, in the absence of any co-circulating SARS-CoV-2 variant, the
vaccine-derived herd immunity threshold needed to eliminate the wild-type strain can be
achieved if 59% of the US population is fully-vaccinated with either the Pfizer or Moderna
vaccine. This threshold increases to 76% if the wild-type strain is co-circulating with the
Alpha variant (a SARS-CoV-2 variant that is 56% more transmissible than the wild-type
strain). If the wild-type strain is co-circulating with the Delta variant (which is estimated
to be 100% more transmissible than the wild-type strain), up to 82% of the US
population needs to be vaccinated with either of the aforementioned vaccines to achieve
the vaccine-derived herd immunity. Global sensitivity analysis of the model reveal the
following four parameters as the most influential in driving the value of the reproduction
number of the variant strain (hence, COVID-19 dynamics) in the US: (a) the infectiousness
of the co-circulating SARS-CoV-2 variant, (b) the proportion of individuals fully vaccinated
(using Pfizer or Moderna vaccine) against the wild-type strain, (c) the cross-protective
efficacy the vaccines offer against the variant strain and (d) the modification parameter
accounting for the reduced infectiousness of fully-vaccinated individuals experiencing
breakthrough infection. Specifically, numerical simulations of the model show that future
waves or surges of the COVID-19 pandemic can be prevented in the US if the two vaccines
offer moderate level of cross-protection against the variant (at least 67%). This study further suggests that a new SARS-CoV-2 variant can cause a significant disease surge in the
US if (i) the vaccine coverage against the wild-type strain is low (roughly <66%) (ii) the
variant is much more transmissible (e.g., 100% more transmissible), than the wild-type
strain, or (iii) the level of cross-protection offered by the vaccine is relatively low (e.g.,
less than 50%). A new SARS-CoV-2 variant will not cause such surge in the US if it is only
moderately more transmissible (e.g., the Alpha variant, which is 56% more transmissible)
than the wild-type strain, at least 66% of the population of the US is fully vaccinated, and the three vaccines being deployed in the US (Pfizer, Moderna, and Johnson & Johnson)
offer a moderate level of cross-protection against the variant.
