Controlling worm propagation in wireless sensor networks: Through fractal-fractional mathematical perspectives

Area of Science:

• Computer Science
• Network Security
• Mathematical Modeling

Background:

• Wireless Sensor Networks (WSNs) face significant malware threats due to resource constraints.
• Existing security models often lack the precision to capture complex malware dynamics in WSNs.

Purpose of the Study:

• To develop a generalized Susceptible-Infectious-Isolated-Protected-Recovered (SIIPR) model for WSNs.
• To incorporate fractional-fractal derivatives for a more realistic malware propagation analysis.
• To analyze the existence, uniqueness, and stability of the proposed model.

Main Methods:

• Utilized an advanced Susceptible-Infectious-Protected-Recovered (SIPR) model with a fractional-fractal derivative (FFD) in the Atangana-Baleanu-Caputo (ABC) sense.
• Introduced a new 'isolated nodes' compartment and associated recovery/isolation parameters.
• Applied nonlinear and fixed-point theory for existence and stability analysis.
• Developed a Newton polynomial-based numerical scheme for approximation.

Main Results:

• Established the existence and uniqueness of solutions for the SIIPR model.
• Performed stability analysis using advanced mathematical theories.
• Demonstrated the model's dynamics through numerical simulations using MATLAB.

Conclusions:

• The proposed fractional-order SIIPR model provides a more accurate representation of malware dynamics in WSNs.
• The findings contribute to developing more robust security strategies for resource-constrained networks.
• The study highlights the importance of advanced mathematical modeling for WSN security.