Modeling the Impact of Dynamic Gastric pH on Helicobacter pylori Eradication and Antibiotic Resistance Emergence

Helicobacter pylori infections present a persistent global health challenge due to increasing antibiotic resistance and the bacterium's ability to survive in the acidic gastric environment. Existing within-host models of H. pylori infection neglect the gastric pH fluctuation, despite its role in modulating bacterial growth and antibiotic efficacy. To address this gap, we extend a published in-host model by explicitly incorporating gastric pH as a dynamic state variable, influenced by three key physiological processes (i) bacterial urease which neutralizes gastric acid to create a protective niche; (ii) host acid secretion response, which attempts to restore baseline acidity; and (iii) dietary perturbations, which induce temporary pH changes. Equilibrium and stability analysis reveal pH-dependent reproductive thresholds $R_s\left(H\right)$ and $R_r\left(H\right)$ that determine the conditions for bacterial persistence and treatment outcome. Successful eradication requires driving both thresholds below unity. Numerical simulations validate distinct clinical scenarios including complete bacterial clearance, resistant strain dominance, stable bacterial coexistence, and oscillatory persistence. These outcomes emerge from the coupled interplay between antibiotic pressure, immune response, and pH regulation. Our model provides a comprehensive theoretical framework for understanding H. pylori treatment failures and highlights how adjuvant pH-modulation strategies could enhance antibiotic efficacy against resistant infections.