A Mathematical Approach for Predictive Cybersecurity in Large-Scale Networks

Abstract

Introduction Day-by-day, Cyberattacks are getting more and more complicated, new malware constantly changes their form, and ransomware often attacks in several stages. Hence, old-style security systems which are reactive after something bad happens are no longer good enough, as they expose the weaknesses in traditional, reactive approaches and show that current security methods are not strong. This paper introduces a new bio- inspired security method called Stateful Propagation Containment. This is inspired by how living things protect themselves. Instead of waiting for an attack to happen and then reacting, this new approach tries to predict problems early and stop them before they occur.Methods The SPC framework draws inspiration from biological self-protection mechanisms and integrates advanced computational techniques, including evolutionary computation and quantum-inspired graph analysis. The research design is theoretical and model-based, comprising five core axioms: (1) Multi Scale Behavioral Baselining for anomaly detection, (2) Evolutionary Threat Prediction to anticipate attacker movements, (3) Quantum-Inspired Correlation Engine to reveal hidden attack connections, (4) Darwinian Defense Engine for adaptive network hardening, and (5) Predictive Surgical Containment for minimally disruptive, three-step isolation of infected systems. Mathematical formulations are provided to demonstrate the reliability and efficiency of each component.Results The theoretical model demonstrates that SPC enables autonomous, self-adjusting network defense capable of preemptively identifying and containing threats before system compromise. Key findings include: the ability to baseline normal network behavior across multiple scales, predict attack propagation paths with evolutionary algorithms, correlate seemingly unrelated attack indicators via quantum-inspired methods, dynamically evolve defense strategies, and enforce containment with near-zero disruption to normal operations.Discussion This paper takes a deep dive into the mathematical formulations that support how the system works and proves that its methods are both reliable and efficient. Besides, it considers the whole system's behavior over time; it is almost like watching how a machine self-adjusts while running like a human would. The concept of SPC is a leap in constructing computer networks that will be able to protect themselves, fix problems on their own, and stop advanced cyberattacks before they get into the network to cause infection. SPC represents a foundational advancement toward realizing autonomous, self-healing network security infrastructures capable of preempting sophisticated cyber threats.