Gastric cancer (GC) remains the third most common cause of cancer-related death worldwide. Infection with Helicobacter pylori is responsible for over 70% of GC incidence; colonization induces chronic inflammation, which can facilitate progression to intestinal metaplasia, dysplasia, and GC (Correa pathway). Although H. pylori eradication is a necessary first step in GC prevention, some patients continue to progress to advanced stage disease if substantial tissue damage has occurred or inflammation persists. This progression is often asymptomatic until cancer reaches stage IV, yet efficient, cost-effective screening protocols for patients who present with early stages of the Correa pathway do not exist. Given the high interpatient heterogeneity in progression time through this pathway, such screening protocols must necessarily be personalized. This requires the identification of reliable and longitudinally assessable biomarkers of patient-specific progression. Several gastric stem cell (GSC) markers including CD44, CD133, and Lgr5 are upregulated in GC. Here we show a significant stepwise increase in immunohistochemical staining for these markers in biopsies at different stages of the Correa pathway, suggesting GSC fraction to be a promising candidate biomarker for early detection of malignant transformation. We present a mathematical model capable of both simulating clinically observed increases in GSC fraction in longitudinal biopsy samples of individual patients, and forecasting patient-specific disease progression trajectories based only on characteristics identified from immunohistochemistry at initial presentation. From these forecasts, personalized screening schedules may be identified that would allow early stratification of high-risk patients, and potentially earlier detection of dysplasia or early-stage GC.