Current farmer. Natural disasters destroy the land. And then nothing grows.

If there was an earth quake, the land gets disrupted (tore apart, split, etc) and you either can't plant into the empty spaces, or need to work the ground which would've taken ages to do back then with animals and small equipment. Large volcanic eruptions have the ash which smothers the land until it floats away or is worked into the ground, and the cooled magma turns into rock which you can't plant into.

Droughts don't just mean lack of water, but rock hard dry earth that you can't plant into. Too wet means plants drown, or quagmires you simply can't get into to plant. Too cold to plant on time means late crops, and if they do get going, your yeilds are reduced because of the shorter growing season.

All of this usually means weaker plants, which are more susceptible to diseases. The plants are not as nutritious, making you weaker and more susceptible to your own diseases. Diseases spread, more people get sick, especially if they're also not getting enough nutrition themselves.

Current farmers still face a lot of stuff from natural disasters. But we do get some lucky breaks now with our current technology (like weather forecasting), equipment size/strength, and how much faster we can do things. And we have also gotten better at producing higher yields of crops, and preventing plant diseases, which ensures the health of animals and people. So humans can flourish, be strong, and thrive.

Gotta use your imagination and critical thinking skills on this one! Think about what happens when flood waters retreat.. the fetid rotting masses of plants and dead animals left behind among wet, festering pools of tepid water... the perfect breeding ground for disease and bacteria.

Natural disasters cause the balance in nature to go awry. This could mean that feeding grounds for normal pests are disturbed so they seek new areas through migration. Locusts coming to areas they've never been historically reported. Small mammals who carry fleas and ticks with disease will look for the easiest food available. If hundreds of thousands of people die, and so quickly that they can't be buried properly, this now will spread disease from the decaying bodies, plus the wildlife that feeds on them. an increase in flies and other insects comes to mind which we know spread bacteria and disease. You also have no humans to clean up and keep rats and mice from getting into the grain supply. In medieval Europe and up to the plague of London in the 17th century, cats and dogs were killed as people thought they were dirty and spread disease. This makes the rat population boom. In that specific case, the plaque was spread from fleas on the rats. More rats, more plaque. Natural disasters have been spreading disease since we have existed.

Drought -> famine -> weaker immune systems because everyone is starving.

It's less a direct cause and more knock on effects.

Its certainly easy to imagine how outbreaks could be facilitated in starving populations.