Abstract:
A novel coronavirus emerged in December of 2019 (COVID-19), causing a pandemic that
inflicted unprecedented public health and economic burden in all nooks and corners of
the world. Although the control of COVID-19 largely focused on the use of basic public
health measures (primarily based on using non-pharmaceutical interventions, such as
quarantine, isolation, social-distancing, face mask usage, and community lockdowns)
initially, three safe and highly-effective vaccines (by AstraZeneca Inc., Moderna Inc.,
and Pfizer Inc.), were approved for use in humans in December 2020. We present a
new mathematical model for assessing the population-level impact of these vaccines
on curtailing the burden of COVID-19. The model stratifies the total population into
two subgroups, based on whether or not they habitually wear face mask in public.
The resulting multigroup model, which takes the form of a deterministic system of
nonlinear differential equations, is fitted and parameterized using COVID-19 cumulative
mortality data for the third wave of the COVID-19 pandemic in the United States.
Conditions for the asymptotic stability of the associated disease-free equilibrium, as
well as an expression for the vaccine-derived herd immunity threshold, are rigorously
derived. Numerical simulations of the model show that the size of the initial proportion of
individuals in the mask-wearing group, together with positive change in behavior from
the non-mask wearing group (as well as those in the mask-wearing group, who do
not abandon their mask-wearing habit) play a crucial role in effectively curtailing the
COVID-19 pandemic in the United States. This study further shows that the prospect
of achieving vaccine-derived herd immunity (required for COVID-19 elimination) in the
U.S., using the Pfizer or Moderna vaccine, is quite promising. In particular, our study
shows that herd immunity can be achieved in the U.S. if at least 60% of the population are fully vaccinated. Furthermore, the prospect of eliminating the pandemic in the U.S. in
the year 2021 is significantly enhanced if the vaccination program is complemented with
non-pharmaceutical interventions at moderate increased levels of compliance (in relation
to their baseline compliance). The study further suggests that, while the waning of natural
and vaccine-derived immunity against COVID-19 induces only a marginal increase in the burden and projected time-to-elimination of the pandemic, adding the impacts of
therapeutic benefits of the vaccines into the model resulted in a dramatic reduction in
the burden and time-to-elimination of the pandemic.
