# How to provide a system of input every x time interval (e.g, x=1 week)

The following code described an input to the system only during t less than minInfusionTime after time zero. Any way to give this same input every x time (e.g. every week) after time of zero, to an ODE system A[t]? In another word, the system receive an input every week, with an input rate of (mgDose/minInfusionTime)

mgDose = 50;
minInfusionTime = 15;
inputSignal =
Function[t,
Piecewise[{{mgDose/minInfusionTime, t < minInfusionTime}}, 0]];


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You can use If and Mod inside NDSolve to achieve this. Here I assume time is measured in hours and there are first-order decay kinetics.

mgDose = 50;
minInfusionTime = 15;
τ = 7*24; (* period *)
tmax = 5 τ;
l = 0.001;

sol = NDSolve[{a'[t] ==
If[0 < Mod[t, τ] < minInfusionTime, mgDose/minInfusionTime, 0] - l a[t],
a[0] == 0}, a, {t, 0, tmax}][[1]];

Plot[a[t] /. sol, {t, 0, tmax}, PlotRange -> All]


• Thank you! Besides Mod, any other approaches? – Math Entry May 10 at 15:26
• If you are OK with an impulsive input instead of one distributed over the finite time minInfusionTime, you could use WhenEvent inside the NDSolve. – Chris K May 10 at 15:37