To contract or get; to show symptoms of an illness.(verb)
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Use "come down with" in a sentence
"By autumn they would have come down with their herds from the mountains to graze lower pastures, so they could have learned the news from Forum Annii."
"Sadly, those most in need of protection—people susceptible to demyelination and paralysis should they come down with an acute infection—are also those most likely to be at risk of severe adverse effects from the very vaccines meant to help them."
"But very little if any fresh air came prisonward, and men continued to come down with fever."