In an epidemic model, the basic reproduction number is $R_0 = \\frac{\\beta N}{\\gamma}$, where $\\beta$ is the transmission rate, $N$ is the population size, and $\\gamma$ is the recovery rate. If a vaccine is introduced that is $90\\%$ effective (i.e., it immunizes $90\\%$ of those vaccinated), and the disease has parameters $\\beta N = 0.6$ days$^{-1}$ and $\\gamma = 0.15$ days$^{-1}$, what is the minimum proportion $p$ of the population that must be vaccinated to achieve herd immunity?