The symptoms are not the illness but the natural healing symptoms of our body trying to expel toxins which are the cause of being ill.

Sniffles, flu, skin rash, pimples, diarrhea, vomiting and more are all ways (behavior) of the body to detox and some of these seem to be contagious, just like laughing or smiling which are not transmissible.

Menstruation moments of woman living together are also said to sync up.

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The mechanism for sniffles and Flu is AFAIK still unknown. Pheromones and exosomes are possible candidates I know of. Some dogs are said to be able to smell if someone is ill.