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.
One frequent problem for European colonists were the diseases in the colonies, diseases they had little defense against without medicines. Back in the day the book was written, this was well known.
Wells frequently uses the railway as a symbol of civilization, how easily it can be overturned, and how it can be repaired. The human complacency in the face of the Martian threat is represented by trains ferrying people to and from the local railway station despite the arrival of extraterrestrial beings. The attack on Woking is symbolised and discussed in terms of the destruction of the station. The great panic is represented by people crowding London's railways stations desperately trying to board a train to safety, and it's mentioned that some drivers are even ploughing their engines through the crowds in their desperation to flee. And at the very end, when the invasion is defeated and life is rebuilding, the narrator returns home by train.
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 where 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 to 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.
The first season of the 1988 television series (an unofficial sequel to the film) works on the premise that the "Martian" doctors and scientists did realize, too late for the original invasion, that Earth microorganisms are deadly to them, and as a result the surviving aliens tend to be forced to nuke themselves with bacteria-destroying radiation to survive and carry out their next invasion, which provides a couple useful plot devices for the series.
This is arguably a case of Fridge Brilliance: if a civilization has entirely wiped out disease and all illness, what's the point of having doctors? They may still have microbiologists, but they'd be serving in pure science roles with none of the medical applications seen today. That infection is even a thing could be limited to microbiologists, but they wouldn't necessarily put together that they can get sick until they look over and see that Gulgulthrapp is flopping out of the hood of his Fighting Machine with a really nasty wheezing cough. That would be the first "oh crap" moment; the second would be recognizing that everyone's been mainlining a major vector for Terrestrial pathogens for weeks now and so everyone is infected. They'd have very little time to reinvent doctoring from the ground up once that realization is made.