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Herd Immunity: Let Ro denote the reproduction number (i.e., the average number of new infections caused by a person, infected with a virus, in the early stages of an outbreak in a fully susceptible population).
Let v denote the fraction of the population with immunity (these are people vaccinated, people who have recovered from the infection, and people who just have immunities naturally). We have 0≤ v≤ 1.
Let Rv=(1-v)Ro . At the extremes, if v=0, then Rv=0 ; and if v=1 , then Rv=Ro. Herd immunity is the value of v such that . That is, the reproduction number falls to less than 1, which means that the disease eventually dies out naturally.
a. Solve (in terms of the reproduction number Ro) for the value of v at which herd immunity occurs. That is, what condition must v fulfill in order to achieve herd immunity?
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