STABILITY ANALYSIS AND POSITIVITY-PRESERVING SIMULATION OF A VACCINATION-BASED MALWARE MODEL IN WIRELESS SENSOR NETWORKS/ АНАЛИЗ УСТОЙЧИВОСТИ И ИМИТАЦИОННОЕ МОДЕЛИРОВАНИЕ ВРЕДОНОСНОГО ПО, ОСНОВАННОГО НА ВАКЦИНАЦИИ, В БЕСПРОВОДНЫХ СЕНСОРНЫХ СЕТЯХ С ЦЕЛЬЮ С
Статья в журнале
ZAFAR A., HUSSAIN SH., FENG X., Sidorov D.N., AHMED I.
Журнал вычислительной математики и математической физики
2026
This study presents a numerical solution of a 2D reaction-diffusion model for malware spread in a wireless sensor network that integrates six compartments of nodes. The model simultaneously accounts for nodes equipped with anti-virus programs, carrier devices, quarantined nodes waning immunity. Through nonlinear analysis, we characterize the system's equilibrium states and establish thresholds governing malware persistence and extinction within the network. A significant computational advancement is achieved via development of a positivity-preserving finite difference scheme, whose mathematical properties are rigorously verified through consistency, stability, and convergence analysis. Numerical simulations reveal the method's capability to resolve complex spatiotemporal transmission patterns while maintaining network reliability. Benchmark tests demonstrate substantial improvements in numerical stability compared to conventional time-integration approaches, particularly under coarse temporal resolution. Practical implementation is validated through investigation of digital network malware spread, employing parameters calibrated from empirical datasets. The results provide quantitative insights for a safe and secure network with efficient protection protocols.
Библиографическая ссылка
ZAFAR A., HUSSAIN SH., FENG X., Sidorov D.N., AHMED I. STABILITY ANALYSIS AND POSITIVITY-PRESERVING SIMULATION OF A VACCINATION-BASED MALWARE MODEL IN WIRELESS SENSOR NETWORKS/ АНАЛИЗ УСТОЙЧИВОСТИ И ИМИТАЦИОННОЕ МОДЕЛИРОВАНИЕ ВРЕДОНОСНОГО ПО, ОСНОВАННОГО НА ВАКЦИНАЦИИ, В БЕСПРОВОДНЫХ СЕНСОРНЫХ СЕТЯХ С ЦЕЛЬЮ СОХРАНЕНИЯ РАБОТОСПОСОБНОСТИ // Журнал вычислительной математики и математической физики. Vol.66. No.10. 2026. P.1733-1759.
