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Thanks for a really nice post and nice work! I've made my own model that includes quarantine but instead of creating a compartment (state variable) for quarantined I simply made beta a time varying function that drops a certain level once quarantine...
I've encountered the same problem with Mathematica v10.0 and .NETLink (evaluateToImage). A "workaround" that's okay for me is to replace PlotTheme->"Web" with Sequence@@DeleteCases[Charting`ResolvePlotTheme["Web", DateListPlot], ...