Solution
= Solution
Since $a,b>0$, the coexistence value $P_*=(\log r)/a$ is positive exactly when $r>1$. Under that condition, $H_*>0$ as well. Therefore the required condition is
$$
\boxed{r>1}.
$$
For $0<r<1$, the formal nonzero candidate has negative parasitoid density and is not biologically admissible; $r=1$ gives only the host-only line of <equilibria>.