Why do some fathers become primary caregivers for their infants? A qualitative study.

West AF, Lewis S, Ram B, Barnes J, Leach P, Sylva K, Stein A; FCCC project team.

Child Care Health Dev. 2009 Mar;35(2):208-16. doi: 10.1111/j.1365-2214.2008.00926.x.

PMID: 19228155

Adult non-response bias from a child perspective. Using child reports to estimate father's non-response. Bastaits K, Pasteels I, Ponnet K, Mortelmans D. Soc Sci Res. 2015 Jan;49:31-41. doi: 10.1016/j.ssresearch.2014.07.004. Epub 2014 Jul 29.

PMID: 25432601

From the father's point of view: how father's representations of the infant impact on father-infant interaction and infant development. Hall RA, De Waard IE, Tooten A, Hoffenkamp HN, Vingerhoets AJ, van Bakel HJ. Early Hum Dev. 2014 Dec;90(12):877-83. doi: 10.1016/j.earlhumdev.2014.09.010. Epub 2014 Oct 21. PMID: 25463835

There italian book about it

https://books.google.it/books/about/Culture_giovanili_Proposte_per_un_interv.html?id=vT0A6nKr4O0C&redir_esc=y

I'm not sure of literature, but in my work there are plenty of NGO's working in countries like Mongolia and Vietnam who will likely have results from research they've conducted. It might be a good idea to contact the NGO's yourself. I would suggest ILO, World Vision, Save the Children, and UNICEF as these organizations tend to have better resources to gather more thorough data.