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Rework formulas/functions to discretize IDE-SECIR model #587

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@annawendler

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@annawendler

Our discretization of the IDE-SECIR model is based on the paper "A non-standard numerical scheme for an age-of-infection epidemic model" by Messina et al. Our discretization formulas are written down in an Overleaf document. In the paper, the infection age as a parameter of the TransitionDistribution (or gamma in our formulas) does not match with the parameter of the transitions (or sigma in the formulas). E.g. when we compute the number of individuals in compartment E at time 0 we take into account the inflow at time 0 but the TransitionDistribution with an infection age of 1. Intuitively, this doesn't make sense. It needs to be discussed if we adapt our formulas and if yes, which ones. The formulas for the compartments do not appear in the paper, so we do not change the approach of the paper when changing these formulas. However, the same problem also occurs when computing the force of infection which is also computed in the paper.

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class::discussionUsed for discussions on software and model .model::ideThis issue concerns any kind of integro differential equations-based model.prio::highThe priority of this task is high.

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