We have compared the efficacy of our proposed Recursive Hybrid model with individual dose-response predictive models at desired time points. 
Recursive Hybrid model
One can easily model the dose-response curve at each time point with Hill equation, but such a model fails to capture the temporal evolution of the curves.  In this article, we propose a parametric model for dose-time responses that follows Gompertz law in time and Hill equation across dose approximately. 
Hill equation
On the other hand, one can use Gompertz equation to model the temporal behaviors at each dose without capturing the evolution of time curves across dosage.



Gompertz equation