The present disclosure provides for recombinant nucleic acids, and cells and virions comprising the recombinant nucleic acids, that can be used to identify, isolate, and/or purify cells latently infected with immunodeficiency virus. A subject recombinant nucleic acid includes (a) a first nucleotide sequence encoding a first reporter polypeptide that produces a first detectable signal, where the first nucleotide sequence is operably linked to an immunodeficiency virus promoter and is translated as an early gene and (b) a second nucleotide sequence encoding a second reporter polypeptide that produces a second detectable signal that is distinguishable from the first detectable signal, where the second nucleotide sequence is operably linked to a non-immunodeficiency virus promoter. In some aspects, the first and second nucleotide sequences are both positioned between a shared 5′ long terminal repeat (LTR) and a shared 3′ LTR. Also provided are related methods.