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

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.