Sneezing is how our body expels things it detects in the sinuses like allergens or other irritants. Viruses and bacteria are just along for the ride. The ones that hang out there had a better chance of spreading and multiplying which means they become more active and ones that don't died out or became less common (or found a different mechanism that helped them spread)

It's kind of neither.

It's important to understand that the virus doesn't "want" anything. It's like a little emotionless and purposeless robot. It reproduces because its programming tells it to reproduce, and that's it. So it's all about that program and what that program tells the virus to do. And occasionally that program up and changes a little thanks to viral mutations.

So let's look at two newly mutated types of virus.

One virus type has a newly written section of program code that triggers the body to sneeze by causing the infected body to generate more mucus and irritate nasal membranes that create the necessary "tickle". In other words, its programming activates our body's natural triggers to have to sneeze. That sneeze will create an aerosol and scatter liquid droplets that contain virus particles. This causes the virus to spread around and cover more real estate.

The other virus type does not share this new programming code. It doesn't trigger sneezing. So, because there are no sneezes, it spreads less effectively.

The first virus's program is more effective at increasing the odds that it will be spread to other hosts... and so it survives and propagates more, while the other virus doesn't spread beyond its initial host as effectively, and propagates less. The first virus doesn't MEAN to do this, it's just the way its programming changed to allow it to spread. And so the virus ends up multiplying in more bodies without "intending" to do so.

It's the result of an accident that's lucky for the virus... but unlucky for us.

Virus infection causes irritation of the nasal cavity, which causes you to sneeze.

The virus and the body do not "want" to do anything as the virus is not alive and the body does not sneez voluntarily. It is just a response built during millions of years of evolution and we still have it today because it increases the chance of survival.

Of course, with simple logic one might deduce that the reason is because sneezing diminishes the viral count on the body.

I guess my question should have been "do viruses cause us to sneeze in order to spread, or do viruses cause us to sneeze because they are irritants?"

In other words, is the body trying to rid itself of the virus? Or is the virus itself causing the sneeze because it has previously benefited from this?

Or, is it both?

*smacks head on wall*

The virus doesn't want anything! It just replicates so often that by chance it got the mutation that will trigger a sneeze (in this case) and this mutation is coincidentally the best one to spread the virus itself (because mutation = just an error of the copy of virus DNA/RNA) so it's the mutation that survives and travel hosts and will be the one you will get.

Think of the virus kinda like mildew - it doesn’t create the environment it needs, it’s just present enough around us that when it happens upon it, it can take advantage and reproduce. Humans create mucus and cough/sneeze to clear things out and keep things in the respiratory tract clear. Cold viruses just happen to be the ones that best spread around in that environment. And once it found its useful environment to live in, if some of the variations figured out how to increase that response, all the better for them. Viruses are all accidents, they find themselves in the right place to take advantage of our mechanisms and vulnerability. You body is trying to clear out mucus and “stuff” that’s blocking its function. The virus is just taking a ride along with it.

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You are being intentionally dense to OPs question. As they noted in the comment you responded to, they recognize there isn’t some active desire in the virus

Their question is whether the virus gains reproductive fitness via phenotypically causing sneezing in its host, or if the act of sneezing is an attempted response by the host to expel virus

They did not know how to phrase it that way, but what they meant is quite clear