An imperfect model (why do you always neglect time...what is it with you and that variable....it's come up time and time again....see that, cute no?). It's pretty clear, in addition to the complications caused by new variants, that both vaccine and natural immunity (from the data Dr. John presents) declines with time. The issue with natural immunity is that not everyone gets the same robust response, but from the Denmark study, it appears to be on every tiered one to one comparison, better and longer lasting than vaccine immunity, but it is declining as well. We don't know how rapidly it is declining, but it seems to decline less severely than vaccine immunity. The vaccine immunity based on the Israeli study and the Oct. 25 2021 Swedish cohort study is declining radically against symptomatic infection and even against severe illness.The area under the case curve decreases if you have a vaccine.
Normally, you keep getting new cases until your recovered population equals the herd immunity threshold.
For this, people who are effectively protected by the vaccine count towards your recovered population.
So, if you need 250 million recovered patients, and 150 million are immune by vaccine, then only 100 million end up getting sick.
Area under the curve fell from 250 to 100.
Harder to explain when you toss in new variants, partially effective natural immunity, and partially effective vaccines, but the core idea is the same. The number of infections is reduced by (number of vaccinated people) x (vaccine efficacy).
Effectiveness of Covid-19 Vaccination Against Risk of Symptomatic Infection, Hospitalization, and Death Up to 9 Months: A Swedish Total-Population Cohort Study
Background: Whether vaccine effectiveness against Coronavirus disease 2019 (Covid-19) lasts longer than 6 months is unclear.<br><br>Methods: A retrospective coh
papers.ssrn.com