If you roughly know the functional family of your input1 (or you are okay with approximating your data), you could actually replace your np.interp (interpolation function) with a partial function b(t), c(t) … like how I did.
I knew my time-varying data follow logistic trends. So I just use logistic functions to model the time-varying trends. If it is sine, cosine… trends (i.e., seasonal flu) maybe such function family is more appropriate.
Of course, doing this way, you will lose some accuracy to your data because interpolation is more flexible/ more precise to your data.