Mathematical Modeling of Giardiasis Transmission Dynamics Using Caputo Fractional Derivative

ABSTRACT Giardia duodenalis is a protozoan parasite that causes giardiasis, a common gastrointestinal infection affecting millions worldwide. Understanding its transmission dynamics is essential for effective prevention and control. This study develops a mathematical model to investigate the spread of giardiasis. The model incorporates key factors, including infection and recovery rates, environmental contamination, sanitation, and treatment measures, and employs a saturated incidence function to account for crowding effects. The disease‐free equilibrium is analyzed, the basic reproduction number is calculated, and stability properties are examined using techniques from dynamical systems. Model parameters are estimated by fitting giardiasis incidence data from Canada from 2005 to 2022. A sensitivity analysis is conducted to identify parameters with the greatest influence on the disease transmission. Numerical simulations illustrate how improved sanitation and treatment can substantially reduce the disease prevalence. The simulation results revealed that the disease dynamics strongly depend on parameters such as the environmental transmission rate, shedding rates, and the progression rate from exposed to infectious/carrier states.