The problem with commenting on this is that what you have here is a very rough draft. You haven't established what sort of leads the party will have or what sort of challenges they will face in investigation. That's the real meat of this campaign, and will be what makes or breaks it. You seem to have a solid premise here, but there's a huge gap (and a lot of prep-work) between a premise and a campaign that's ready to run.
One thing I would warn against is red herrings. With an open-ended adventure like this, the PC's are going to find their own trees to bark up, so it's generally not advisable to add your own distractions. You also need to tread a very delicate balance with adventures like this. You don't want to give away the answer too early, but you also want to make sure that your players don't get stuck in a dead-end or chasing down a rabbit hole after they jumped to conclusions. The key thing to remember is this rule of thumb: activities undertaken by the PC's should progress the plot. This means that any red herrings you include should ultimately direct the players in the right direction if they investigate it. Similarly, you should include lots of information and leads to direct the players along the right course of investigation.
There's a great rule of thumb called the "three clue rule". For anything you want your players to figure out, always include at least three redundant clues that set them along the right path. Have an eye for points of failure in your adventure. Always consider the possibility that players might miss something that is plot critical, or misunderstand its significance. If you find such a point of failure, fix it by including other avenues (generally at least three in total) that will substitute if the players miss the first one. This isn't foolproof, since players can miss all three clues, but the idea is to limit the number of situations in which the GM has to actively step in and railroad.
Red herrings are fine, particularly in a sandbox game. A wild goose chase is always a good way get the PCs some levels on their way to ending the campaign. The trick is to make sure at some point the PCs see the red herring for a red herring. If the PCs think the disease/curse is caused by vampires (but it isn't) they need to eventually know that. Otherwise, they will be chasing their tails over and over.
One thing you could do is make the campaign ending problem something in the background until its appropriate for them to deal with. In the beginning of the game, the PCs hear about some terrible plague on the other side of the world. Though that's not on their radar right now as they are working on fortune and fame or whatever right here at home. As the campaign progresses, the plague spreads to their part of the world and now they have to deal with it.
All false leads, red herrings, wild goose chases should lead back to the cause. Let's say it is a secret guild poisoning people (the Herbalists Guild trying to drive up prices for their goods). The group discovers that a powerful wizard's apprentices have been spending a lot of time with the diseased people. This makes the party think that it is a curse by the wizard.
But, no, the wizard is actually trying to diagnose the disease, not causing it. Not only that, but the wizard should be able to tell the group that while he doesn't know what the disease is, he can tell them that it isn't magical in nature.
Next, suppose the group suspects a particular deity because their clerics have been conspicuously absent from helping the diseased. Their investigation should lead them to the various churches and the discovery that the absent clergy have been dealing with an internal heresy or an unrelated crop blight or somesuch. But the party's investigation should yield the information that no deity is punishing the people with a disease.
Each wrong lead should not only prove false but completely shut down that line of reasoning. Not only is it not that wizard, it isn't any wizard. Not only is it not that god, it isn't any god. By process of elimination, they get closer and closer to the truth as fewer and fewer possibilities remain.
I'm just starting to prepare it, we are supposed to play it next summer.
Then you have plenty of time to prep. It's more a matter that I can only comment on what you've provided at this point, which is just the premise.
The idea of multiple theories was mostly to make it more realistic. If the NPCs new what was the real source, someone else would have taken the task to fix it by now. Of course any "wrong" route they would follow would still lead to great treasures, XP, and possibly clues on the real source.
That last part is the important part. The actions of your PC's should progress the plot. The point isn't for the PC's to always be right (I'd agree that would be a bad table dynamic) but rather that their actions always progress the story's narrative and never send them back to the beginning.
One important caveat with realism is that in real life a lot of mysteries go unsolved. That may reflect reality, but it doesn't make for a good story and thus this should be avoided in our games. This doesn't mean that you can't have loose ends or mysteries that don't get answered, but the main plot point should be designed to be solveable by the PC's to create a satisfying narrative experience. It's the same reason why we don't have 1st level characters encounter Troll Warbands. That may be a realistic fate for adventurers in-universe, but not very conductive for a good story.
Since solving the issue should be the end-game objective, I can't just constantly give them clues or it would end too soon. I could give them side quests, but they could just ignore them.
Any tips?
You want to have intervening plot points between your premise and resolution. Right now you have a premise (there is a plague) and a resolution (party cures the plague). If you want to stretch out the plot, you need to expand upon intervening plot points to add more connecting points between A and B.
Red herrings are fine, particularly in a sandbox game. A wild goose chase is always a good way get the PCs some levels on their way to ending the campaign.
I wouldn't say to never use them, but I would warn against them. In my experience, players will find their own red herrings without you having to intentionally create them. I feel that if you're taking time to prepare it as part of the overarching campaign, it should always tie into that campaign somehow.
Each wrong lead should not only prove false but completely shut down that line of reasoning. Not only is it not that wizard, it isn't any wizard. Not only is it not that god, it isn't any god. By process of elimination, they get closer and closer to the truth as fewer and fewer possibilities remain.
I would go one step further; in the process of their investigation the party should find evidence that directs them towards the herbalist guild. For instance, suppose they investigate a cult performing evil rituals. It turns out that the cultists are also afflicted with the disease and are trying to cure themselves. They even had some limited success with a strange mixture of blood from human sacrifices and some unknown exotic herbs.
So even though the cult isn't responsible, the party has found some hints at a possible cure and is directed towards the herbalists for further investigation. This directly pushes the plot forward and sets the players on the right track, even if they don't know it yet.