Neco Model Questions Vol1 2020 Biology Question 2

An outbreak of a disease occurs in a community of \(10{,}000\) people. The first week there are \(5\) confirmed cases. Each infected person infects, on average, \(R_{0}\) new persons per week. After three weeks the cumulative number of cases is \(150\). Assuming discrete weekly generations and a constant \(R_{0}\), determine the approximate value of \(R_{0}\). A vaccination programme is then introduced that reduces the effective reproduction number by \(40\%\). Starting from the end of week three, estimate the total number of cases that will have occurred by the end of week five (i.e., after two more weeks) under the reduced reproduction number. Round the final number of cases to the nearest whole person.