Before revision:  We show that these cause the  reproduction number to decrease with progression , and consequently have a drastic effect on the estimate of the necessary percentage of the population that has to contract the disease for herd immunity to be reached.
After revision:  We show that these cause the effective reproduction number to decrease with progression , and consequently have a drastic effect on the estimate of the necessary percentage of the population that has to contract the disease for herd immunity to be reached.