A Mathematical Model of <i>Helicobacter</i><i> </i><i>pylori</i> Transmission Incorporating Antibiotic Resistance

<i>Helicobacter</i><i> </i><i>pylori</i> (<i>H.</i><i> </i><i>pylori</i>) infection remains a major public health concern, particularly in developing countries with inadequate sanitation. The increasing rate of antibiotic resistance complicates treatment, prolongs infections, increases household transmission, and raises the risk of complications like stomach ulcers, highlighting the need for improved interventions. This study develops and analyzes a mathematical model of <i>H.</i><i> </i><i>pylori</i> transmission that incorporates antibiotic resistance, classifying infectious individuals into drug-sensitive, drug-resistant, and stomach ulcer cases. Individuals with drug-sensitive infections are treated with <i>first-line</i> antibiotics, those with drug-resistant infections are treated with <i>second-line</i> antibiotic therapy, and patients infected with stomach ulcer cases undergo specialized antibiotic management. Moreover, the transition from drug-resistant to drug-sensitive cases occurs as treatment suppresses resistant strains, letting sensitive strains dominate. Analytical results show that the basic reproduction number ℜ<i><sub>c</sub></i>; is the sum of two reproduction numbers ℜ<i><sub>s</sub></i> and ℜ<i><sub>r</sub></i> representing the contribution of the sensitive and resistant strains, respectively. The disease-free equilibrium is locally asymptotically stable when ℜ<i><sub>c</sub></i><1, indicating possible eradication under effective control measures, while the endemic equilibrium is stable when ℜ<i><sub>c</sub></i>>1, implying persistent transmission. Sensitivity analysis identifies critical parameters that influence the persistence of <i>H.</i><i> </i><i>pylori</i> in the population. Numerical simulations demonstrate that improved hygiene and sanitation, together with the use of appropriate and timely antibiotic therapy, significantly reduce the prevalence of sensitive and resistant strains, limit stomach ulcer development, and lower the overall infection burden.