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I am wondering what the set of differential equations is that is used to model how viruses spread in a population?

I am also wondering how epidemiologists get around the highly irregular shape of a country to make more-or-less accurate predictions.

There seem to be a couple possible approaches that come to mind, one being a partial differential model based on density and time over a spatial distribution, but as well a system of several ordinary differential equations that resemble logistical modeling.

The most likely set of equations seems to be something pertaining to what is mentioned here

https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread-of-disease-the-differential-equation-model

but this also mentions logistical-appearing variants.

I have seen others related to reaction-diffusion and second-order partial differential models.

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