An Age-Structured Model of COVID-19 Analyzing the Impact of Vaccinations in the US

The COVID-19 pandemic since its onset in 2019 continues to upend different countries in a cyclical manner through the emergence of new variants of the virus. While different approaches including masking, social distancing and quarantining have been directed at slowing or stopping the spread of the virus, the most effective has been vaccination. So far, all COVID-19 vaccines have been breached by the virus and its variants. Therefore current vaccines do not provide full immunity but are mostly successful in controlling the virus by reducing the disease severity when a vaccinated person gets infected. Vaccine administration, availability and hesitancy has plagued some communities and as a consequence allowed the virus to continue to spread. The longevity of the protection generated by the vaccines also appear to be very limited thus requiring booster shots. Further, certain age groups do not yet have an approved vaccine. This paper presents an age-structured mathematical model of the transmission dynamics of COVID-19. We consider 16 age groups, each spanning five years and use systems of differential equations to simulate the disease under various vaccine regiments. The high transmissibility of the virus is demonstrated through computations of the reproduction number \(R_0\) . Numerical simulations closely agree with the recent CDC findings that about \(60\%\) of the US population has had COVID-19, with about \(75\%\) of children 11 and younger. Also, model simulations of cumulative COVID-19 deaths before and after the introduction of vaccines in the US are in close agreement with reported data.