they were neglected in the previous simple form of the model (dubbed eQP in [@Pes05]). Additionally, damping contributions were neglected as they are small at zero chemical potential, $\mu=0$.

The procedure of mapping the eQP results from $\mu=0$ into the $T$-$\mu$ plane is plagued by some ambiguities leading to non-unique solutions close to the presumed phase transition. Therefore, the model is restricted to sufficiently large temperatures. First attempts to include collective excitations into a two-flavor quasiparticle model at nonzero chemical potential have been made [@RR03] and suggest that these ambiguities might vanish. In this work we show that both collective excitations and damping effects are necessary to preserve the self-consistency of the model and ensure unique solutions when extrapolating towards large baryon densities at moderate temperatures. In the present work, the 2+1 flavor case is considered, allowing the use and extrapolation of recent lattice data [@Kar07].

Our paper is organized as follows. Section \[sec:derivation\] will comprise the derivation of the full HTL-based QPM, including collective modes and damping, as a series of approximations from QCD. The necessary further approximations leading to the eQP and its problems are discussed in section \[sec:eQP\]. The results for both models are then contrasted in 