Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 6A / d / Solution

At the leading edge $S\simeq 1$ and $I$ is small, soSeek a decaying mode $I\sim e^{-\lambda \xi }$ with $\lambda >0$. Its characteristic equation isA nonoscillatory positive leading edge requires real positive roots, henceFor an invasive infection, $mu<1$, and the selected minimum speed is thereforeIf $\mu \ge 1$, the state ahead of the wave is below the epidemic threshold and no growing infection front is selected.