Hilfer-Katugampola fractional epidemic model for malware propagation with optimal control

The rise in everyday internet users worldwide can be ascribed to advancements made to the internet worldwide. Attacks by malware cause data loss, hardware destruction, and large financial losses. As a result, this research creates a novel mathematical compartmental dynamical model that, under both fixed and dynamic size network assumptions, can be utilized to precisely predict malware outbreaks. The modeling processes divided the network into seven distinct states and considered the diverse ways that users of the internet interacted with potentially hazardous links. The Hilfer-Katugampola fractional operator was employed to obtain the intended varied states of networks. The existence, uniqueness, equilibrium, and stability of the provided models are thoroughly examined. Then the best control plan is implemented for every network topology. The controllers' objectives are to minimize the costs of data loss due to infections, malware tracing, and public awareness improvements. Ultimately, we confirm the theoretical results by observing the spread of malware using numerical simulations. Results demonstrated the effectiveness of the enforced control measures in maintaining the necessary goals of malware infection management.