Neco 2019 Agricultural Science Question 45

In a poultry farm of \(200\) birds, a contagious disease has a transmission coefficient \(\beta = 0.8\) day\(^{-1}\) per infected bird and an average infectious period of \(4\) days. Initially, \(2\) birds are infected. (a) Estimate the number of new infections expected after one infectious period using the approximation \(\text{new infections} \approx R_0 \times I_0\), where \(R_0 = \beta \times \text{infectious period}\). (b) If a vaccination programme reduces the susceptibility of the flock by \(60\)%, compute the effective reproduction number \(R_{\text{eff}}\) and state whether the outbreak will be controlled. (c) Determine the minimum vaccination coverage (as a percentage) required to bring \(R_{\text{eff}}\) below 1.