An infection has basic reproduction number in a well-mixed population

PHYSICS · Subjective · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems

Many Parts, One Behaviour, Ch Epidemics on networks

Problem

An infection has basic reproduction number R0=4R_0 = 4 in a well-mixed population. A vaccine confers immunity to a fraction ϵ=0.85\epsilon = 0.85 of those who receive it (its efficacy), and immune individuals cannot transmit or acquire the infection. What fraction of the population vcv_{\rm c} must receive the vaccine to reach herd immunity?

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