Optimal Control Strategies for a Fractional Leprosy Model With Environmental Bacterial Load

ABSTRACT In this study, we introduce a mathematical model to analyze the dynamics of leprosy transmission, incorporating a novel SEIR framework extended by an additional compartment that accounts for the bacterial load in the environment. The model employs the Caputo–Fabrizio (CF) fractional derivative to better represent memory effects in the disease transmission process. We establish the existence and uniqueness of the solution using the Banach fixed‐point theorem and analyze both the local and global stability of the equilibrium states. A comprehensive sensitivity analysis is conducted to identify the key parameters influencing the spread of leprosy. Numerical simulations are performed to demonstrate the model's ability to capture the complex dynamics of leprosy transmission. Additionally, an optimal control strategy is proposed, involving two control variables: raising awareness and administering medical treatment to reduce the number of infected individuals. Results reveal that awareness‐raising is more effective than treatment alone, as it promotes early diagnosis and limits further transmission. Simulations confirm that the fractional order serves as a control parameter influencing convergence to equilibrium and infection persistence. Overall, the findings provide valuable insights into leprosy management, highlighting the importance of environmental factors and public health interventions.