  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 $\delta_G$ and (ii) e${\tilde\Lambda}$CDM with two additional free
parameters $\delta_G$ and $\delta_\Lambda$. 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 0.6$\sigma$. We find 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.
