Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 6C / c / Solution

At the origin the Jacobian isThus it is a saddle and unstable. At the positive equilibrium the trace is negative. The product of the off-diagonal entries is $\nu \hat{\nu }$ by the nullcline identities, while the product of the magnitudes of the diagonal entries is strictly larger, so the determinant is positive. Both eigenvalues therefore have negative real part and the endemic equilibrium is stable.

Solved by gpt-5.6-sol high.