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

## TL;DR

This paper proposes a new mathematical model using fractal-fractional calculus to better understand and control malware spread in wireless sensor networks.

## Contribution

The paper introduces a modified SIPR model with an isolated compartment and uses fractional-fractal derivatives for more accurate malware propagation analysis.

## Key findings

- The proposed SII1PR model with FFD provides a more realistic representation of malware dynamics in WSNs.
- Existence, uniqueness, and stability of the model's solutions were theoretically established.
- Numerical simulations using MATLAB confirmed the model's effectiveness in capturing malware behavior.

## Abstract

Wireless Sensor Networks (WSNs) are particularly vulnerable to malware attacks due to their limited processing power, memory, and energy, which makes defending against such threats especially challenging. To mitigate these serious security issues caused by malware infection, various preventive measures can be implemented, such as honeypots, robust security protocols, hardware-based protections, regular updates, firewalls, and intrusion detection systems (IDS). Considering these security concerns, we adopt an advanced version of the existing susceptible–infectious–protected–recovered SIPR model that incorporates a fractional-fractal derivative (FFD) defined in the Atangana-Baleanu-Caputo (ABC) sense, which offers a more realistic representation than the classical model. Furthermore, this research work introduced a new isolated nodes compartment 𝐈1, along with parameters γ2 and δ1, defining the recovery and isolation rates of 𝐈1, respectively, in the existing SIPR model. Moreover, this study focuses on the existence and uniqueness of solutions, stability analysis, control theory and numerical approximation for the proposed generalized susceptible–infectious isolated-protected–recovered SII1PR model. Additionally, nonlinear and fixed-point theory are used to obtain the results of existence and stability analysis. On the same line, Newton polynomial-based numerical scheme was established for the proposed modified model. The dynamics of desired results are visualized using MATLAB.