  The recent results from the first year baryon acoustic oscillations (BAO)
data released by the Dark Energy Spectroscopic Instrument (DESI), combined with
cosmic microwave background (CMB) and type Ia supernova (SN) data, have shown a
detection of significant deviation from a cosmological constant for dark
energy. In this work, we utilize the latest DESI BAO data in combination with
the SN data from the full five-year observations of the Dark Energy Survey and
the CMB data from the Planck satellite to explore potential interactions
between dark energy and dark matter. We consider four typical forms of the
interaction term $Q$. Our findings suggest that interacting dark energy (IDE)
models with $Q \propto \rho_{\rm de}$ support the presence of an interaction
where dark energy decays into dark matter. Specifically, the deviation from
$\Lambda$CDM for the IDE model with $Q=\beta H_0\rho_{\rm de}$ reaches the
$3\sigma$ level. These models yield a lower value of Akaike information
criterion than the $\Lambda$CDM model, indicating a preference for these IDE
models based on the current observational data. For IDE models with
$Q\propto\rho_{\rm c}$, the existence of interaction depends on the form of the
proportionality coefficient $\Gamma$. The IDE model with $Q=\beta H\rho_{\rm
c}$ yields $\beta=0.0003\pm 0.0011$, which essentially does not support the
presence of the interaction. In general, whether the observational data support
the existence of interaction is closely related to the model. Our analysis
helps to elucidate which type of IDE model can better explain the current
observational data.
