A Perturbation and Symmetry-Based Analysis of Mobile Malware Dynamics in Smartphone Networks

In this paper, we present a mathematical model, Msiqr, to analyze the dynamics of mobile malware propagation in smartphone networks. The model segments the mobile device population into susceptible, exposed, infected, quarantined, and recovered compartments, integrating critical control parameters such as infection and quarantine rates. The analytical results include the derivation of the basic reproduction number, R0, along with equilibrium and stability analyses that provide insights into long-term system behavior. A focused scenario analysis compares the baseline dynamics with a more aggressive malware variant and a more effective quarantine response. The results show that increased infectivity sharply escalates the peak of infection, while enhanced quarantine measures effectively suppress it. This highlights the importance of prompt containment strategies even under more virulent conditions. The sensitivity analysis identifies the infection rate as the most influential parameter driving peak infection, while the quarantine rate exerts the most significant dampening effect. Monte Carlo simulations of parameter uncertainty reveal a consistently high epidemic potential across varied conditions. A parameter sweep across the infection–quarantine space further maps out the conditions under which malware outbreaks can be mitigated or prevented. Overall, the model demonstrates that mobile malware poses sustained epidemic risk under uncertainty, but effective control parameters—particularly quarantine—can drastically alter outbreak trajectories.