NP-completeness of Induced disjoint paths

In graph theory, it is well-known to be NP-complete the problem of given a set of $ k$ pairs of source-sink, deciding whether there exists $ k$ vertex-disjoint paths connecting these pairs.

Our problem is a variant in which the requirement of being vertex-disjoint is replaced by being induced.

Input: A graph $ G(V,E)$ and $ k$ pairs of source-sink $ \{(s_1,t_1),\dots,(s_k,t_k)\}$

Output: YES if there exists (a set of) $ k$ induced paths connecting $ s_i$ to $ t_i$ for every $ 1\leq i\leq k$ , NO otherwise.