A team led by scientists at the University of California, San Francisco, and Carnegie Mellon University tracked how much sleep 164 healthy adults actually got for a week, then deliberately exposed all of them to a cold virus under quarantine.
People who had slept fewer than five hours a night had about four and a half times the odds of developing a clinical cold compared with those sleeping more than seven hours, and the pattern held even after accounting for age, stress, smoking, and antibody levels measured before exposure.
Because sleep was measured with a wrist monitor over real nights rather than reported from memory, and because exposure to the virus was controlled rather than left to chance, the study could link short sleep to illness more directly than most. It could not say whether occasional short nights carry the same risk as chronic short sleep, a question left for future work.

Read the original study
Short sleep, better odds for a virus.
Source
- Prather, A. A., Janicki-Deverts, D., Hall, M. H., & Cohen, S. (2015). Behaviorally Assessed Sleep and Susceptibility to the Common Cold. Sleep, 38(9), 1353–9. https://doi.org/10.5665/sleep.4968