Disappointing ODE integration

Any general linear method that is unconditionally positivity preserving for all positive ODEs must have order ≤ 1.

https://arxiv.org/pdf/2005.06268.pdf

This is unfortunate. Order 1 is not accurate enough to solve a typical infectious disease dynamics problem at a scale where the outputs are relevant. That’s why many ODE integration schemes in our fields have added checks that the increments do not make any compartment negative.