Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 6A / b / Solution

The infective equation isSince $X\le N$, the threshold population isIf $N<N_c$ and $\delta =\mu +\nu -\beta N>0$, thenAlsoAny steady state with $Y>0$ would require $X=N_c>N$, which is impossible. Thus the infection cannot be maintained, and both infected and immune populations tend to zero from every admissible initial condition.