A Nielsen-Reidemeister index is constructed for multivalued maps defined by fractions $f/p$ where $p: \tilde X \to X$ is a fibrewise manifold with closed fibres over a compact ENR and $f:\tilde X\to X$ is a continuous map. In the case that $p$ is a finite $n$-fold cover, this index is shown to agree with the index of the $n$-valued map $\tilde X\multimap \tilde X$ associated with $f/p$ by a construction of Brown .
"Nielsen-Reidemeister indices for multivalued maps." Bull. Belg. Math. Soc. Simon Stevin 24 (4) 483 - 499, december 2017. https://doi.org/10.36045/bbms/1515035003