Computational models predicting symptomatic progression at the individual level can be highly beneficial for early intervention and treatment planning for Alzheimers disease (AD). Individual prognosis is complicated by many factors including the definition of the prediction objective itself. In this work, we present a computational framework comprising machine-learning techniques for 1) modeling symptom trajectories and 2) prediction of symptom trajectories using multimodal and longitudinal data. We perform primary analyses on three cohorts from Alzheimers Disease Neuroimaging Initiative (ADNI), and a replication analysis using subjects from Australian Imaging, Biomarker & Lifestyle Flagship Study of Ageing (AIBL). We model the prototypical symptom trajectory classes using clinical assessment scores from mini-mental state exam (MMSE) and Alzheimers Disease Assessment Scale (ADAS-13) at nine timepoints spanned over six years based on a hierarchical clustering approach. Subsequently we predict these trajectory classes for a given subject using magnetic resonance (MR) imaging, genetic, and clinical variables from two timepoints (baseline + follow-up). For prediction, we present a longitudinal Siamese neural-network (LSN) with novel architectural modules for combining multimodal data from two timepoints. The trajectory modeling yields two (stable and decline) and three (stable, slow-decline, fast-decline) trajectory classes for MMSE and ADAS-13 assessments, respectively. For the predictive tasks, LSN offers highly accurate performance with 0.900 accuracy and 0.968 AUC for binary MMSE task and 0.760 accuracy for 3-way ADAS-13 task on ADNI datasets, as well as, 0.724 accuracy and 0.883 AUC for binary MMSE task on replication AIBL dataset.