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Since I personally would count mass starvation as a disaster, that one would be pretty easy to link with plants. And a related type of "slow moving" disaster linked with plants is soil erosion, dont know what you mean with "model", what type of model do you want, what do you want to use it for?
If you want a physical model to have for a school project or something similar then I could suggest doing an erosion model, a guy did that in my class when I was a kid, although it might be too simple for some higher level classes. On a flat slightly tilted surface, place a piece of rugged cloth (like a towel or something), put 1dL of dirt on it, then put 1dL of dirt on a square of similar size next to it. Then gently pour 1dL of water on each patch. The patch with the rugged cloth will still have loads of dirt left locked in the fibers of the cloth. While the pure dirt layer will be almost all washed off. The idea here being that the cloth with it's threads and fibers represent roots from plants, and if you remove the plants the soil are much more easily washed away by water from rains and floods etc. And less soil makes it harder or impossible to grow crops on the land, which in turn might cause the farmers to clear more land from other growth (forests etc) to be able to keep up their crop production.
U give me an idea and I will give u one. This time our house will defeate urs. Alll the best!!!!!!!!