  We investigate an extended cosmological model motivated by the asymptotic
safety of gravitational field theory, in which the matter and radiation
densities and the cosmological constant receive a correction parametrized by
the parameters $\delta_G$ and $\delta_\Lambda$, leading to that both the
evolutions of the matter and radiation densities and the cosmological constant
slightly deviate from the standard forms. Here we explain this model as a
scenario of vacuum energy interacting with matter and radiation. We consider
two cases of the model: {(i) ${\tilde\Lambda}$CDM with one additional free
parameter $\delta_G$, with $\delta_{\rm G}$ and $\delta_\Lambda$ related by a
low-redshift limit relation and (ii) e${\tilde\Lambda}$CDM with two additional
free parameters $\delta_G$ and $\delta_\Lambda$ that are independent of each
other.} We use two data combinations, CMB+BAO+SN (CBS) and CMB+BAO+SN+$H_0$
(CBSH), to constrain the models. We find that, in the case of using the CBS
data, neither ${\tilde\Lambda}$CDM nor e${\tilde\Lambda}$CDM can effectively
alleviate the $H_0$ tension. However, it is found that using the CBSH data the
$H_0$ tension can be greatly relieved by the models. In particular, in the case
of e${\tilde\Lambda}$CDM, the $H_0$ tension can be resolved to 0.71$\sigma$. We
conclude that as an interacting dark energy model, ${\tilde\Lambda}$CDM is much
better than $\Lambda(t)$CDM in the sense of both relieving the $H_0$ tension
and fitting to the current observational data.
