Igcse Model Questions Vol1 2019 Biology Question 25

In a closed community of 5\,000 people an outbreak of a respiratory infection occurs. The first case appears on day 0. By day 7 there are 150 new cases, by day 14 there are 600 new cases and by day 21 there are 1\,800 new cases. Assume the infection follows a discrete generation model with a generation length of 7 days, so that the number of new cases in each generation follows \(C_{n+1}=R_{0}\,C_{n}\). Using the data from generations 1 to 3, estimate the basic reproduction number \(R_{0}\) (give your answer to two decimal places). Then, if a vaccination programme reduces the proportion of susceptibles to 30 % before the outbreak, would the outbreak be expected to grow? (Answer "yes" if the effective reproduction number \(R_{e}=R_{0}\times S\) is greater than 1, otherwise "no".) Provide the value of \(R_{0}\) and the yes/no answer.