Fuzzy-fractional modeling and analysis of virus propagation in wireless sensor networks via He-Laplace framework

The propagation and spread of computer viruses is a significant threat that greatly affects network security. By closely examining the diffusion patterns of viruses in wireless sensor networks (WSNs), the future can be predicted, and preventive measures can be taken to avoid network damage. This manuscript presents modeling the transmission characteristics of computer viruses in WSNs within a fuzzy-fractional framework. The fractional derivative is taken in Caputo sense throughout the manuscript. Also, triangular fuzzy numbers (TFNs) are utilized to incorporate uncertainties in the virus model. This approach is aligned with real scenarios because mathematical model of virus outbreak in WSNs contains uncertain patterns. A semi-numerical scheme is proposed for the solution and analysis purposes. This approach includes multiple homotopies along with perturbation process and Laplace transform to derive series-form solutions for different wireless nodes. The obtained solutions offer a clear understanding of how proposed methodology addresses virus propagation at lower and upper bounds. Moreover, detailed error analysis is conducted to validate the obtained results in fuzzy and non-fuzzy contexts, demonstrating the ability of proposed algorithm to capture the complexities of the network problem. Additionally, a comprehensive graphical analysis is performed to investigate the behavior of wireless nodes within the fuzzy-fractional framework. The fractional parameter is particularly examined under various constraints and assumptions and presented as 2D, 3D plots and gradient contour diagrams. This investigation confirms the effectiveness of hybrid approach in handling uncertainties related to the unpredictable in WSNs, and deepening our understanding of ongoing challenges related to virus transmission. This approach also applicable to other complex models encounter in different fields.