Emergency calls are defined by an ever-expanding utilisation of information and sensing technology, leading to extensive volumes of spatio-temporal high-resolution data. The spatial and temporal character of the emergency calls is leveraged by authorities to allocate resources and infrastructure for an effective response, to identify high-risk event areas, and to develop contingency strategies. In this context, the spatio-temporal analysis of emergency calls is crucial to understanding and mitigating distress situations. However, modelling and predicting crime-related emergency calls remain challenging due to their heterogeneous and dynamic nature with complex underlying processes. In this context, we propose a modelling strategy that accounts for the intrinsic complex space-time dynamics of some crime data on cities by handling complex advection, diffusion, relocation, and volatility processes. This study presents a predictive framework capable of assimilating data and providing confidence estimates on the predictions. By analysing the dynamics of the weekly number of emergency calls in Valencia, Spain, for ten years (2010-2020), we aim to understand and forecast the spatio-temporal behaviour of emergency calls in an urban environment. We include putative geographical variables, as well as distances to relevant city landmarks, into the spatio-temporal point process modelling framework to measure the effect deterministic components exert on the intensity of emergency calls in Valencia. Our results show how landmarks attract or repel offenders and act as proxies to identify areas with high or low emergency calls. We are also able to estimate the weekly average growth and decay in space and time of the emergency calls. Our proposal is intended to guide mitigation strategies and policy.