In this study we investigate a novel quantitative instrument for the development of intervention strategies for disease modifying drugs in Alzheimer's disease. Our framework is based on the modeling of the spatio-temporal dynamics governing the joint evolution of imaging and clinical biomarkers along the history of the disease, and allows the simulation of the effect of intervention time and drug dosage on the biomarkers' progression. When applied to multi-modal imaging and clinical data from the Alzheimer's Disease Neuroimaging Initiative our method enables to generate hypothetical scenarios of amyloid lowering interventions. The results quantify the crucial role of intervention time, and provide a theoretical justification for testing amyloid modifying drugs in the pre-clinical stage. Our experimental simulations are compatible with the outcomes observed in past clinical trials, and suggest that anti-amyloid treatments should be administered at least 7 years earlier than what is currently being done in order to obtain statistically powered improvement of clinical endpoints.