Mathematical modeling of the effects of screening and treatment of gastric ulcers as a control strategy for gastric cancer

Glory Kawira Mutua; Musyoka Kinyili; Dominic Makaa Kitavi; Glory Kawira Mutua; Musyoka Kinyili; Dominic Makaa Kitavi

doi:10.3934/mbe.2026040

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 4: 1067-1095. doi: 10.3934/mbe.2026040

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Mathematical modeling of the effects of screening and treatment of gastric ulcers as a control strategy for gastric cancer

1.
Department of Mathematics and Statistics, University of Embu, Kenya
2.
School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
3.
College of Computer Studies, De La Salle University, Philippines

Received: 17 July 2025 Revised: 21 December 2025 Accepted: 30 January 2026 Published: 09 March 2026

Gastric cancer is among the most common cancers in the world, and it has a significant negative impact on the health and economies of different countries, led by those that are developing. This study formulates a deterministic model for the transmission dynamics of gastric cancer through gastric ulcers, incorporating screening and treatment strategies. The model is thoroughly analyzed both quantitatively, qualitatively, and numerically. The key properties considered in the model analysis are positivity, invariant region, equilibria, stabilities, and bifurcation analysis. We compute the control reproduction number $ \mathcal R_{C} $ using the next-generation matrix approach. This enables us to prove that the model has a unique disease-free equilibrium (DFE) and admits a unique endemic equilibrium, which are locally and globally asymptotically stable whenever $ \mathcal R_{C} < 1 $ and $ \mathcal R_{C} > 1 $, respectively. Sensitivity analysis indicates that increasing the rate of screening decreases the control reproduction number, consequently reducing the rate of transmission of infections. Simulation results demonstrate that the combination of screening and treatment is the most effective intervention in reducing infection transmission. Furthermore, a combination of early screening and treatment proves more effective than a combination of late screening and treatment of gastric ulcers. Screening the infected population alone is identified as the least effective strategy for curtailing transmission of infection in the susceptible population. The findings of this study will guide public health officers in making decisions regarding the screening and treatment of exposed individuals with Helicobacter pylori infection and gastric ulcer patients, therefore aiding in fighting gastric ulcers and their progression to gastric cancer.
- gastric cancer,
- gastric ulcers,
- mathematical modeling,
- control reproduction number,
- deterministic models,
- numerical simulations
Citation: Glory Kawira Mutua, Musyoka Kinyili, Dominic Makaa Kitavi. Mathematical modeling of the effects of screening and treatment of gastric ulcers as a control strategy for gastric cancer[J]. Mathematical Biosciences and Engineering, 2026, 23(4): 1067-1095. doi: 10.3934/mbe.2026040

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Abstract

Gastric cancer is among the most common cancers in the world, and it has a significant negative impact on the health and economies of different countries, led by those that are developing. This study formulates a deterministic model for the transmission dynamics of gastric cancer through gastric ulcers, incorporating screening and treatment strategies. The model is thoroughly analyzed both quantitatively, qualitatively, and numerically. The key properties considered in the model analysis are positivity, invariant region, equilibria, stabilities, and bifurcation analysis. We compute the control reproduction number $ \mathcal R_{C} $ using the next-generation matrix approach. This enables us to prove that the model has a unique disease-free equilibrium (DFE) and admits a unique endemic equilibrium, which are locally and globally asymptotically stable whenever $ \mathcal R_{C} < 1 $ and $ \mathcal R_{C} > 1 $, respectively. Sensitivity analysis indicates that increasing the rate of screening decreases the control reproduction number, consequently reducing the rate of transmission of infections. Simulation results demonstrate that the combination of screening and treatment is the most effective intervention in reducing infection transmission. Furthermore, a combination of early screening and treatment proves more effective than a combination of late screening and treatment of gastric ulcers. Screening the infected population alone is identified as the least effective strategy for curtailing transmission of infection in the susceptible population. The findings of this study will guide public health officers in making decisions regarding the screening and treatment of exposed individuals with Helicobacter pylori infection and gastric ulcer patients, therefore aiding in fighting gastric ulcers and their progression to gastric cancer.

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