Yora, you might look at the bat, rat, and otyugh monster entries for some ideas. As a caveat, I wouldn't introduce into the game any natural disease more virulent than those conferred via sorcery (contagion, inflict disease, etc.).

i think it can vary a little with strain but it malaria can be contracted multiple times, but generally if the victim survives the first time they will fair better on later bouts.

But do most groups have a cleric or druid of 5th level or higher?
Depending on how fast the group levels up, it can easily be 20 play sessions or more until any character reaches 5th level. I've only ever played two campaigns in which characters advanced that far, in 15 years of running games. And when a cleric dies, it may take some more time until a replacement joins the group and makes it to 5th level. And such a 5th level cleric can cast only one or two 3rd level spells per day. When you're in a jungle with a dozen carriers for supplies, curing five members of the party of a disease would take 3 to 5 days, and that's if the cleric is willing to accept being unable to cast any other 3rd level spells for that duration.
I would not outright dismiss something just because there's a spell for it.

I did some more research and plague and cholera seem to provide decent immunity if you survive it. Reinfections are known to have happened, but seem to be quite unusual.
Malaria results in higher resistance against further infections, but it last only for a couple of years if a person is not exposed to it.
Typhus only increases resistance, but does not result in immunity. Tuberculosis does not result in immunity.

Since campaigns usually don't span very long periods of time, I think malaria can be treated as resulting in immunity like cholera and plague.
Another important thing, as I see it, is that a cure disease spells just makes the disease "magically go away". Therefore the immune system never overcame the infection and the individual does not gain immunization. Which makes the highly contagious plague and cholera almost impossible to fight magically. You can heal a person every few days, but you can't make the epidemic go away until virtually everyone has either died or successfully fought off the disease.
Irrelevant in the case of rabies, since there is no way to survive it without magic. (The first known case of a person surving rabies is from 2006. The treatment required extensive use of highly advanced medicine and even that method seems to be able to save a person in about a third of all cases.)

Now the remaining big question would be what actual effect on the character these diseases have. I have to say the d20 method seems to be a quite neat solution.

Mostly as an added complication for overland travel. Death isn't even a desires outcome, as far as I am concerned. If a charactet dies from bad luck, that isn't entertaining for everyone. But if the fighter has to carry the sick mage as the party is fleeing from angry natives or a priest has to instruct a thief how to perform a ritual to calm an insulted spirit, I think it adds a huge amount of flavor to the adventure.
Good thing you mentioned this. Whatever the rules, they shouldn't be too deadly or incapacitating on the PCs. (They are PCs, they are ment to carry on where normal people reach their limits.)

My original idea was to punish players for ignoring tents and blankets once the summer reaches its end, but turns out the typical popular diseases caused by living in horrible conditions are significantly more awful than a really bad cold.

Cholera could still show up when a PC falls into sewage. And I think typhus can be used to created added horror when dealing with mistreated prisoners. It's of course nice when the PCs drag half starved slaves from a dungeon, but the risk of catching an infection should add another level of discomfort.
And plague just is THE classic... well, plague. One of the campaign ideas I've been carrying around for some time is a game set in a region during a bad plague epidemic. Social disruption and complete breakdown is the most important part, but the risk of catching it makes navigating such an environment much more tense. From a fiction perspective, plague is awesome. Towns and villages with 80% casualties, the sudden disappearance of most of the ruling class, total lack of town security, unguarded castles, drifting ships full of cargo and corpses. Imagining returning from an adventure and the village you've been passing through two weeks ago is completely empty and you simply cross the town square and carry on immediately.
A most fascinating environment.

I'm also working on a streamlined rules system for overland travel, use custom encumbrance, and try to figure out a different way to deal with wealth.
I should make my own retroclone.

But I think a 20 page, system-neutral book for Adventuring might be an actual possibility.

I don't have a lot of interest in a hardcore simulation of Late Antiquity when it comes to all of the nasty ways you could die from infection and disease, but I do have a few simple rules for dealing with diseases and sickness and I tie it directly to the PCs decision about how much money they are willing to spend on monthly upkeep.

In a nutshell, I check once every game month to see if the PC has been exposed to some kind of contagion (bad food, bad water, infectious disease, whatever) If players tell me before-hand that they want to live on the cheap in squalid conditions or camp out, then the chance is 10% (1-4gp per month of upkeep), if they want to spend enough to live at "barely adequate/peasant" level (5-10gp per month) then the chance for exposure drops to 4%. If they pick an average upkeep level (or higher) then the chance drops down to 2%.

But even with exposure, the PC always gets a Save vs. Death to see if they contract the disease, and even without a cure disease spell, there are almost always herbal concoctions that can be procured that will allow a new Save vs. Death.

Basically, I don't want the game to get bogged down into too much realism (else every cut and scratch in a fight should have the chance to fester and turn into an infection) but this gives the players some agency as they have to balance their greed vs. how much risk they want to expose their characters to.

On those rare occasions when somebody has actually contracted something at low level, I've been able to turn that into a hook - an herbalist sends them out to go collect a certain, hard to acquire mountain flower, a toad-stool from the swamp, etc.

One caveat, if players go wading into a swamp or sewer, or run into a plague victim, there's an instant check for exposure and (if exposed) a Save vs. Death.