Optimal Defense Strategies Against Ransomware With Quantum Acceleration

Abstract

This paper presents a comprehensive mathematical framework for modeling ransomware propagation and control across networked systems. We develop an eight-compartment model that captures the sequential stages of ransomware attacks: initial infection, scanning, lateral movement, encryption, ransom demand, final impact, malware propagation, and recovery. The model uses ordinary differential equations to analyze key factors including infection spread rates, detection times, and system recovery. We derive the basic reproduction number R0 and perform stability analysis to determine conditions for outbreak control ( R0 < 1 ) versus persistence ( R0 > 1 ). Sensitivity analysis reveals that the proportion of infected systems becoming new malware sources (parameter m ) most strongly influences outbreak potential. We extend the model to incorporate quantum computing effects, introducing quantum-enhanced malware and quantum-resistant defenses. Optimal control strategies are developed using Pontryagin’s Maximum Principle to minimize system damage while balancing intervention costs. Numerical simulations demonstrate that quantum threats can increase the reproduction number by 281%, while quantum defenses can reduce this amplification by 29%. The results provide actionable insights for cybersecurity policy, emphasizing early intervention and quantum-aware defense strategies.