لَا عَدْوٰى وَلَا طِيَرَةَ. (Mishkat al-Masabih: 4577)
Meaning: Disease does not spread independently, and evil omens have no reality.
Independently means by its own power apart from Allah's will. What is denied here is that kind of independent effect, not the possibility of disease transmission.
1. An evil omen: treating something as a bad sign of coming misfortune.