OBRENOVAC, Serbia — For five days, as rain pelted the Balkans and the waters rose, Jovanka Sreckovic, 85, waited in bed in her tiny house, barely a hut, beside the Sava River. Ms. Sreckovic, unable to walk, had no food, no water, no medicine and no electricity, and felt herself sinking into sickness with nothing but a children’s book about Jesus to pass the time.

And then, on Saturday, a squad of frantic police officers from neighboring Montenegro bashed in her front door and snatched her away so fast that she had no time to grab a pair of shoes. She even had to leave her precious cat, Rosa, behind.

“I had not been able to get out of my bed, even to look outside,” said Ms. Sreckovic, a retired schoolteacher. “So I was shocked to see that the water had come to within a few yards of my front door. I would have drowned in less than an hour.”

The worst of the waters have receded, for the moment, even here in the Serbian town hit hardest by the record-smashing floods. But with temperatures in the mid-80s and rising, concerns are now shifting to an almost inevitable outbreak of disease in the coming weeks.