# A Perturbation and Symmetry-Based Analysis of Mobile Malware Dynamics in Smartphone Networks
## 2 Related Work  
The study of mobile malware propagation has evolved significantly in recent years, with researchers developing various mathematical models to understand and predict malware spread patterns. Complex network theory has been applied to mobile phone virus propagation [24], establishing a foundation for network-based malware modeling. This work demonstrated how network topology influences infection dynamics but did not incorporate quarantine mechanisms or distinguish between different disconnection pathways that characterize modern mobile security protocols. Epidemiological frameworks have been extended to investigate the impact of cyber-security awareness on mobile malware propagation [25]. These approaches highlighted the importance of user behavior in malware containment, yet the models lack explicit quarantine compartments and do not differentiate between natural device turnover and malware-induced disconnections. This limitation reduces the model's applicability to scenarios where active isolation strategies are employed. Network automata approaches have been developed for modeling malware spread over SMS networks [26], focusing on discrete-time dynamics and cellular communication vectors. While these methods capture SMS-specific propagation mechanisms, they do not address the continuous-time dynamics essential for real-time malware response systems, nor do they incorporate recovery pathways that account for both direct recovery and post-quarantine rehabilitation. Recent advances in malware modeling have explored more sophisticated compartmental structures. Epidemiological-inspired models for self-propagating malware have emerged as powerful tools for understanding cyber threats [27], demonstrating how traditional epidemic frameworks can be adapted to cyber security, yet these approaches lack mobile-specific considerations such as device mobility and network heterogeneity. Quarantine strategies in networks with heterogeneous immunity have been investigated [28], focusing on network-level isolation mechanisms but not addressing device-specific quarantine states that characterize mobile security protocols. Traditional SIRA (Susceptible, Infected, Removed, Antidotal) models have been extended to incorporate quarantine mechanisms [29], although these approaches primarily focus on network-level isolation rather than the dual recovery pathways observed in mobile environments. SEIRS-based models for mobile device malware propagation have been developed to capture reinfection dynamics [30], yet they typically assume homogeneous device populations and do not differentiate between various disconnection mechanisms that characterize mobile networks. Comprehensive frameworks for mathematical models of malware propagation have been proposed [31], highlighting the need for more sophisticated approaches that capture network complexity. However, these models often lack the granular treatment of mobile-specific characteristics such as device turnover and malware-induced performance degradation. The SUIQR (Susceptible, Undetectable, Infected, Quarantined, Recovered) model has been developed [32], representing a significant advancement in incorporating quarantine dynamics for wireless sensor networks, yet this model does not address the dual recovery pathways observed in mobile environments. SEIRS-NIMFA models for IoT networks have been proposed [33], focusing on latency periods in malware propagation, but these approaches do not distinguish between natural device turnover and malware-induced disconnections. Comprehensive reviews of mathematical models for malware propagation [34] reveal that most existing approaches are based on ordinary differential equations but fail to capture individual device characteristics and dynamic behaviors, a limitation particularly pronounced in mobile environments where device heterogeneity, user behavior variability, and network mobility patterns significantly influence malware spread dynamics. Despite these advances, the existing models exhibit several critical gaps.