  Discrete-time models are the traditional approach for capturing population
dynamics of a host-parasitoid system. Recent work has introduced a
semi-discrete framework for obtaining model update functions that connect
host-parasitoid population levels from year-to-year. In particular, this
framework uses differential equations to describe the hosts-parasitoid
interaction during the time of year where they come in contact, allowing
specific behaviors to be mechanistically incorporated into the model. We use
the semi-discrete approach to study the effects of host-feeding, which occurs
when a parasitoid consumes a potential host larva without ovipositing. Our
results show that host-feeding by itself cannot stabilize the system, and both
the host and parasitoid populations exhibit diverging oscillations similar to
the Nicholson-Bailey model. However, when combined with other stabilizing
mechanisms such as density-dependent host mortality or density-dependent
parasitoid attack rate, host-feeding expands the region of parameter space that
allows for a stable host-parasitoid equilibrium. Finally, our results show that
host-feeding causes inefficiency in the parasitoid population, which yields a
higher population of hosts per generation. This suggests that host-feeding may
have limited long-term impact in terms of suppressing host levels for
biological control applications.
