An interactive notebook for a simple SEIR model

[giordano]

The documentation of the Python package uncertainties (which does linear error propagation like Measurements.jl) has some words about this:

The standard deviations and nominal values calculated by this package are thus meaningful approximations as long as uncertainties are “small” . A more precise version of this constraint is that the final calculated functions must have precise linear expansions in the region where the probability distribution of their variables is the largest . Mathematically, this means that the linear terms of the final calculated functions around the nominal values of their variables should be much larger than the remaining higher-order terms over the region of significant probability (because such higher-order contributions are neglected).

For example, calculating x*10 with x = 5±3 gives a perfect result since the calculated function is linear. So does umath.atan(umath.tan(x)) for x = 0±1, since only the final function counts (not an intermediate function like tan() ).

Another example is sin(0+/-0.01) , for which uncertainties yields a meaningful standard deviation since the sine is quite linear over 0±0.01. However, cos(0+/-0.01) , yields an approximate standard deviation of 0 because it is parabolic around 0 instead of linear; this might not be precise enough for all applications.

More precise uncertainty estimates can be obtained, if necessary, with the soerp and mcerp packages. The soerp package performs second-order error propagation: this is still quite fast, but the standard deviation of higher-order functions like f(x) = x3 for x = 0±0.1 is calculated as being exactly zero (as with uncertainties ). The mcerp package performs Monte-Carlo calculations, and can in principle yield very precise results, but calculations are much slower than with approximation schemes.