Dynamic Modeling of Malware Attack and Defense Using the Laplace‐Adomian Decomposition Method

ABSTRACT Malware propagation in computer networks poses a critical cybersecurity challenge that demands mathematically rigorous defense frameworks. In this paper, a fractional‐order e‐SIQR (susceptible, infected, quarantined, recovered) malware‐spreading model using Caputo fractional derivatives of order μ (0 < μ < 1) is proposed to investigate the dynamics of malware infections that incorporate memory and hereditary properties of the natural infection process. The system has a total number of N nodes divided into four groups having an initial configuration of S(0) = 50, I(0) = 25, Q(0) = 25, and R(0) = 0 and parameter values comprising the infection rate β = 0.01, quarantine rate γ = 0.04, recovery rate δ = 0.05, and crash rates α 1 = 0.1 and α 2 = 0.2. The LADM is considered a semianalytic method that avoids linearization and discretization while quickly yielding a series solution. R 0 is obtained using the next‐generation matrix technique. It has been shown that a malware‐free equilibrium is locally asymptotically stable whenever R 0 < 1. Two optimal control variables, U 1 (preventive shielding) and U 2 (quarantine screening), are formulated using Pontryagin's maximum principle to minimize infection while optimizing resource deployment. MATLAB simulations demonstrate that the LADM solution, truncated at three terms, closely matches the fourth‐order Runge–Kutta method, with enhanced convergence at lower fractional orders reflecting memory‐driven dynamics. Results confirm that strategic quarantine and anti‐malware measures substantially reduce infection peaks and accelerate recovery, offering actionable guidance for cybersecurity professionals in designing layered network defenses.