Matching instantaneous rate at time t to the aggregated counts over (t-1,t]

[mhoehle]

SEIR-model-Stockholm/Script/Estimate_SEIR_for_sharing_new_incidence_2020_05_05.R

Line 244 in abd5bc3

fitted_incidence <- p_symp * fit_E * eta

I was wondering if the matching between observed number of cases y_t on day t (which is the aggregated number of cases between time t and time t+1) and the instantaneous number of E->I transitions at time t shouldn't be done by

y_t = \int_{t}^{t+1} (1-p_0) \rho E(u) du

instead. Of course one can approximate this integral by (1-p_0) \rho E(u) as in an Riemann-type approximation, but if there is some change within one day (like when there is exponential increase) it would make a difference. Not sure the difference is worthwhile, and there might be bigger issues, but since you share your code ont GitHub it seems like worth mentioning.

[FohmAnalys]

Thank you for this comment. We tried this before (or rather y_t = \int_{t-1}^{t} … ) and got basically the same estimates for the tested scenario. With basically I mean the same up to 4 or 5 decimals. Do you think it should vary more?

[martisak]

My two cents on this - while it's good that the estimates didn't change here, the case highlighted by @hoehleatsu could perhaps happen for some other input data. So if someone tries to run this code on new input data, then this update could possibly help them.