Adaptive mathematical modeling for predicting and analyzing malware

In this paper, we propose and investigate an improved mathematical model of malware propagation in network structures based on a modification of the well-known raw-immune-response susceptible-infected-recovered (SIR) model. For detailed numerical analysis, our study introduces the fourth-order Runge-Kutta method, which provides higher accuracy in determining fundamental parameters such as infection, recovery and immunity loss coefficients of network nodes. The obtained simulation results demonstrate that the peak of the epidemic occurs when 34.7% of all nodes are infected, with a peak after 32.5-time units. The main contribution of this work is the in-depth understanding and quantification of cyber threats, which emphasizes the importance of prompt response, regular system software updates, and continuous monitoring of network activity. This research makes a significant contribution to cybersecurity applications by providing quantitative tools and strategies to help strengthen network defenses against malicious attacks. The identified patterns and their numerical interpretation can be integrated into processes for optimizing measures to prevent the widespread spread of malware, thereby enhancing the overall security and stability of networked systems.