Caputo approach to transmission dynamics of paragonimiasis in humans, snails, and crustaceans

Paragonimiasis, a parasitic infection caused by trematodes of the genus Paragonimus, is characterized by chronic cough, chest pain, and hemoptysis. This study introduces a novel fractional-order modelling technique to capture the impact of memory effects and control strategies on the transmission dynamics of Paragonimiasis. We develop a system of Caputo fractional differential equations supplemented with constant control measures–specifically, human treatment to reduce infection prevalence and snail molluscicide to target intermediate hosts. We analyze the fundamental properties of the model, including positivity, boundedness, existence, and uniqueness of solutions. Local stability of equilibrium states is investigated via Routh’s criterion, while Ulam-Hyer’s stability concepts confirm global stability. Numerical solutions obtained through the Adams-Bashforth-Moulton predictor-corrector method highlight the considerable influence of memory on disease progression. The results underscore the importance of integrating memory effects into control strategies: enhanced human treatment combined with improved snail molluscicide can significantly mitigate infection levels. These findings suggest that fractional derivatives offer a flexible, detailed lens for examining nonlocal disease dynamics processes and refining practical intervention approaches.