Helicobacter pylori (H. pylori) 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 H. pylori 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 first-line antibiotics, those with drug-resistant infections are treated with second-line 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 ℜc; is the sum of two reproduction numbers ℜs and ℜr representing the contribution of the sensitive and resistant strains, respectively. The disease-free equilibrium is locally asymptotically stable when ℜc<1, indicating possible eradication under effective control measures, while the endemic equilibrium is stable when ℜc>1, implying persistent transmission. Sensitivity analysis identifies critical parameters that influence the persistence of H. pylori 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.
| Published in | American Journal of Mathematical and Computer Modelling (Volume 11, Issue 2) |
| DOI | 10.11648/j.ajmcm.20261102.11 |
| Page(s) | 81-97 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Helicobacter Pylori, Drug-sensitive Strain, Drug-Resistant Strain, Antibiotic Resistance, Reproduction Number, Numerical Simulation
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APA Style
Mwanthi, V. K., Karanja, S., Njagi, L., Kimathi, M. (2026). A Mathematical Model of Helicobacter pylori Transmission Incorporating Antibiotic Resistance. American Journal of Mathematical and Computer Modelling, 11(2), 81-97. https://doi.org/10.11648/j.ajmcm.20261102.11
ACS Style
Mwanthi, V. K.; Karanja, S.; Njagi, L.; Kimathi, M. A Mathematical Model of Helicobacter pylori Transmission Incorporating Antibiotic Resistance. Am. J. Math. Comput. Model. 2026, 11(2), 81-97. doi: 10.11648/j.ajmcm.20261102.11
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Download@article{10.11648/j.ajmcm.20261102.11,
author = {Vincent Kyunguti Mwanthi and Stephen Karanja and Loyford Njagi and Mark Kimathi},
title = {A Mathematical Model of Helicobacter pylori Transmission Incorporating Antibiotic Resistance},
journal = {American Journal of Mathematical and Computer Modelling},
volume = {11},
number = {2},
pages = {81-97},
doi = {10.11648/j.ajmcm.20261102.11},
url = {https://doi.org/10.11648/j.ajmcm.20261102.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20261102.11},
abstract = {Helicobacter pylori (H. pylori) 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 H. pylori 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 first-line antibiotics, those with drug-resistant infections are treated with second-line 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 ℜc; is the sum of two reproduction numbers ℜs and ℜr representing the contribution of the sensitive and resistant strains, respectively. The disease-free equilibrium is locally asymptotically stable when ℜcc>1, implying persistent transmission. Sensitivity analysis identifies critical parameters that influence the persistence of H. pylori 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.},
year = {2026}
}
TY - JOUR T1 - A Mathematical Model of Helicobacter pylori Transmission Incorporating Antibiotic Resistance AU - Vincent Kyunguti Mwanthi AU - Stephen Karanja AU - Loyford Njagi AU - Mark Kimathi Y1 - 2026/04/24 PY - 2026 N1 - https://doi.org/10.11648/j.ajmcm.20261102.11 DO - 10.11648/j.ajmcm.20261102.11 T2 - American Journal of Mathematical and Computer Modelling JF - American Journal of Mathematical and Computer Modelling JO - American Journal of Mathematical and Computer Modelling SP - 81 EP - 97 PB - Science Publishing Group SN - 2578-8280 UR - https://doi.org/10.11648/j.ajmcm.20261102.11 AB - Helicobacter pylori (H. pylori) 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 H. pylori 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 first-line antibiotics, those with drug-resistant infections are treated with second-line 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 ℜc; is the sum of two reproduction numbers ℜs and ℜr representing the contribution of the sensitive and resistant strains, respectively. The disease-free equilibrium is locally asymptotically stable when ℜcc>1, implying persistent transmission. Sensitivity analysis identifies critical parameters that influence the persistence of H. pylori 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. VL - 11 IS - 2 ER -
Department of Mathematics, Meru University of Science and Technology, Meru, Kenya
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