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Multi-band observations of the fast radio burst (FRB) 131104 show that thisburst may be associated with a gamma-ray transient entitled Swift J0644.5-5111.Follow-up observations for potential X-ray and radio counterparts of FRB131104/Swift J0644.5-5111 got null results and provided the upper limits of theemission flux at 5.5 GHz, 7.5 GHz, $U$-band, and X-ray band. By assuming thisassociation and using these upper limits, environmental properties (thefraction of energyin a magnetic field $\varepsilon_{\rm B}$ and the numberdensity $n$) of the progenitor system of FRB 131104/Swift J0644.5-5111 wereconstrained in the context of the standard afterglow model that neglects thenon-relativistic effect and jet effect by several groups. In this paper, weadopt a unified afterglow model that takes into account the non-relativisticeffect and jet effect and use the upper limits of four bands (5.5 GHz, 7.5 GHz,$U$-band, and X-ray) to obtain more stringent constraints on the parameterspace spanned by $\varepsilon_{\rm B}$ and $n$. We thus suggest that FRB131104/Swift J0644.5-5111 might originate from a black hole-neutron star mergerevent. Moreover, we calculate multi-band emissions from a kilonova powered bythe radioactivity of $r$-process elements synthesized in the ejectedneutron-rich material and find that the $U$-band emission from the putativekilonova is significantly lower than the upper limit of the observations.

Constraining the Environmental Properties of FRB 131104 Using the Unified Dynamical Afterglow Model