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All Journal Indonesian Journal of Electrical Engineering and Computer Science
Dwi Ely Kurniawan
Politeknik Negeri Batam Gunadarma University

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A mathematical model for IoT malware propagation with adaptive patching strategy based on R₀: a simple optimal control approach Dwi Ely Kurniawan; Sarifuddin Madenda; Eri Prasetyo Wibowo
Indonesian Journal of Electrical Engineering and Computer Science Vol 43, No 1: July 2026
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v43.i1.pp219-232

Abstract

This paper presents a mathematical framework for modeling and controlling internet of things (IoT) malware propagation via an adaptive patching strategy governed by the real-time basic reproduction number R₀. We introduce the SEIR-P (susceptible–exposed–infected–recovered–patched) model, where the patching control rate u(t) is a sigmoid feedback function of R₀(t). All epidemiological parameters are calibrated from three empirical malware captures of the IoT-23 dataset (Stratosphere laboratory, Czech Technical University) a publicly available labeled collection of real IoT network traffic comprising 23 captures from infected and benign devices: CTU-IoT-1 (Mirai), CTU-IoT-9 (Torii), and CTU-IoT-17 (IRCBot) yielding the first empirically grounded parameter set for SEIR-type IoT epidemic models with confidence intervals. The optimal control problem is formulated via pontryagin’s maximum principle (PMP), and a closed-form R₀(u) expression is derived via the next-generation matrix (NGM), yielding the critical threshold u_crit = 0.142 day⁻¹. Five comparative simulation scenarios over a 365-day horizon show that the proposed R₀-adaptive strategy achieves a 91.3% reduction in peak infection (360 vs. 4,142 devices), eradicates malware by day 179, and attains the highest cost-effectiveness index (CEI = 1.142). Global asymptotic stability of the disease-free equilibrium under u*(t) is proven via Lyapunov’s method and LaSalle’s Invariance Principle. PRCC sensitivity analysis identifies u_max and β as dominant parameters. This closed-loop framework bridges the gap between abstract epidemic theory and deployable IoT security management.
Co-Authors Eri Prasetyo Wibowo, Eri Prasetyo Sarifuddin Madenda