In the book it's mentioned that for all the technology the Martians never seem to have invented something as simple as the wheel, what are the Martians so fascinated by when we see them outside their tripods? A bicycle wheel.
A lot of people complain about the ending — where the Martians die suddenly of diseases resulting from Earth's bacteria that they are no longer immune to — as being a Deus ex Machina that comes out of nowhere to solve the plot. Read the first chapter again. Literally the first paragraph of the book — and every adaptation which draws on it — compares the way the Martians look at humanity to the way humans look at bacteria; dispassionately, as something small, insignificant, easily dismissed or forgotten about. And yet any expert will tell you that in the right conditions bacteria can be devastating. The ending was hinted at right from the beginning... and if you forgot about it, you made the exact same mistake the Martians made.
Are we suppose to assume the aliens have no doctors or any kind of treatment? I know its in the original novel that germs kill them, but H.G. Wells wrote it at a time when antibiotics let alone effective treatments and isolation were not known. Medical science was not really advanced at the time so Wells could not assume a future were invading armies were free of this risk. An invading army from space would have access to stuff we cannot yet conceive yet they fail to take basic precautions in an alien environment for them.
Multiple sources from the musical adaptation of the original novel state that the aliens had wiped out any form of disease on their planet, and thus eliminated the need for medical science (at least the kind that treated infections or diseases). So they just didn't think to prepare, or their immunity was that low after centuries of not facing infections at all that they were all terminal before they could get anyone to research a cure.
The book also mentions that the aliens wiped out all disease and germs on Mars, leaving them vulnerable to earth's microbes. Further, they feed by injecting human blood directly into their veins, which would be a major infection source if anything (blood transfusion was not well understood back then).
The Doylist answer is that the book is an allegory about British colonialism and imperialism at the time, and that the invaders so outmatched the defenders technologically (as the British frequently did) that they were Nigh Invulnerable to military assault, but that each new world (or part of ours) has its own unique diseases and afflictions which can destroy a force attempting ton conquer it (or destroy the people you're trying to conquer). Basically, Welles was saying "Yeah, smallpox is only fun when it's not happening to you." The Watsonian explanation could very well be that Martian medical science was indeed so advanced that paradoxically they were completely unprepared for any significant infections, or that the Earth diseases were so virulent to Martian physiology that there was just no chance of finding a cure before they all dropped dead. If they didn't even realize they were sick until they became symptomatic, and died very shortly after showing symptoms, no one in the Martian command structure would have had any idea what was going on, let alone what to do about it, until it was too late.