Current therapies against ulcers caused by H. pylori infection consist of antibiotics, an acid reducer, and some clinical trials underway to develop a H. pylori vaccine. We develop a structured model with age-dependent mortality of peptic ulcers and H. pylori infection. Our main goal is to analyze our structured model mathematically and to compare it to our previously unstructured model to examine the disease transmission dynamics in terms of annual prevalence and annual incidence of the disease.