What question did this study set out to answer?

This research aims to explore the dynamics of disease transmission using a fractional-order model, highlighting the impact of environmental factors and delays.

June 26, 2026Open Access

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

Key Points

This research aims to explore the dynamics of disease transmission using a fractional-order model, highlighting the impact of environmental factors and delays.
Developed a fractional-order epidemic model utilizing Caputo derivatives and time delays.
Performed qualitative analysis, including stability and existence of solutions, for the model equations.
Conducted sensitivity analysis to determine key parameters influencing disease dynamics.
Identified key parameters affecting the basic reproduction number, crucial for stability analysis.
Establish conditions for disease eradication under specific transmission dynamics.
Numerical simulations validated analytical findings, demonstrating the effectiveness of proposed control strategies.

Abstract

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.

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