Enhancing Short-Term Sensitivity in Daily-Level Forecasting with Facebook Prophet

I have a daily time series dataset, and I'm using Facebook Prophet for daily-level predictions. Frequently, my actual data experiences sudden spikes due to external events. What I want to achieve is to capture the sharp increase in the very short term and then gradually return to a more typical level in the short to medium term.

I've been able to accomplish this to some extent using a state space model, but I'm facing challenges with Prophet. It seems that Prophet doesn't effectively consider the concept of locality, meaning it doesn't account for the most recent data in the way I desire.

How can I achieve this specific forecasting behavior using Facebook Prophet?