Fractional caputo modeling of delayed disease dynamics: sensitivity analysis and control strategies incorporating environmental influences

This study presents a fractional-order epidemic model incorporating Caputo derivatives and time delays to capture the environmental effects and incubation periods inherent in disease transmission dynamics. We analyzed the qualitative properties of the system, such as the existence, uniqueness, and boundedness of solutions, ensuring both mathematical consistency and biological relevance. The basic reproduction number is derived as a threshold parameter governing the stability of equilibria. Local and global stability analysis of the disease-free and endemic equilibria has been discussed, revealing conditions for disease eradication or persistence. Furthermore, sensitivity analysis is performed to identify the most influential parameters affecting the threshold parameter and transmission dynamics, providing valuable insights for designing effective control strategies. Numerical simulations are presented to illustrate and validate the analytical results.