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We develop a Spatio-TEMporal Mutually Exciting point process with Dynamic network (STEMMED), i.e., a point process network wherein each node models a unique community-drug event stream with a dynamic mutually-exciting structure, accounting for influences from other nodes. We show that STEMMED can be decomposed node-by-node, suggesting a tractable distributed learning procedure. Simulation shows that this learning algorithm can accurately recover known parameters of STEMMED, especially for small networks and long data-horizons. Next, we turn this node-by-node decomposition into an online cooperative multi-period forecasting framework, which is asymptotically robust to operational errors, to facilitate Opioid-related overdose death (OOD) trends forecasting among neighboring communities. In our numerical study, we parameterize STEMMED using individual-level OOD data and county-level demographics in Massachusetts. For any node, we observe that OODs within the same drug class from nearby locations have the greatest influence on future OOD trends. Furthermore, the expected proportion of OODs triggered by historical events varies greatly across counties, ranging between 30%-70%. Finally, in a practical online forecasting setting, STEMMED-based cooperative framework reduces prediction error by 60% on average, compared to well-established forecasting models. Leveraging the growing abundance of public health surveillance data, STEMMED can provide accurate forecasts of local OOD trends and highlight complex interactions between OODs across communities and drug types. Moreover, STEMMED enhances synergies between local and federal government entities, which is critical to designing impactful policy interventions.