At the disease-free <equilibrium point> $(1,0)$, the <linearization of a dynamical system> of the infected equation is $\dot y=(\beta-d)y$. Thus \b[exponential invasion occurs exactly when] $\boxed{\beta>d}$. At equality there is no positive linear growth rate; the nonlinear boundary dynamics described below do not give sustained invasion.

Solution

Past exam of the mathematics course of the University of Cambridge / 2015 / ii / Paper 3 / 11E / b / Solution

 Solution (source code)