THE PERSISTENCE OF AN AGE-STRUCTURED SYPHILIS MODEL

Syphilis, a highly infectious bacterial infection, poses a significant health threat globally due to its high morbidity and mortality rates. Predominantly transmitted through sexual contact, the age distribution among hosts plays a pivotal role in the disease transmission dynamics. In this paper, we first formulate an age-structured epidemic model with four infection stages (primary, secondary, latent and tertiary) and then derive the explicit expression of the basic reproduction number by using the next generation equation. According to the definition of the persistence and applying advanced mathematical techniques, including multiple integral reordering, variable transformations, Laplace transforms, and the method of contradiction, we not only prove the weak persistence but also the strong persistence of the disease.