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<p>Recently, Wireless Sensor Networks (WSNs) have proven their pivotal role across several domains, such as battlefield surveillance, patient monitoring, and climate data collection. However, implementing security solutions in WSNs is very challenging due to the inherent constraints of computing power, memory, and energy in sensor nodes. To develop a novel epidemic-inspired compartmental model, five unique states: susceptible (S), exposed (E), two infectious classes (I₁ and I₂), and recovered (R) (SEI<sub>1</sub>I<sub>2</sub>R), serve as the basis to capture the malware propagation dynamics in WSNs. In contrast to classical approaches, our approach introduces a dual infection model, where exposed nodes transition into either I₁ or I₂ with distinct probabilities, enabling the realisation of real-world-like conditions of two distinct malware behaviours. Furthermore, the effects of node density (<i>ρ</i>) and the communication radius (<i>r</i>) are also probed for malware transmission by integrating them with the infection rate explicitly. A key contribution of this research is the derivation of the basic reproduction number (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{R}_{0}^{th}\)</EquationSource> </InlineEquation>). It is considered a key threshold parameter that delineates the malware propagation in WSNs, apprehending the local dynamics of malware transmission. Furthermore, the expressions for threshold node density and communication radius are derived and validated through simulation results. Rigorous mathematical analysis establishes that the malware-free equilibrium is locally and globally stable whenever the basic reproduction number <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:{R}_{0}^{th}\)</EquationSource> </InlineEquation> is less than unity, whereas the endemic equilibrium emerges and remains stable when <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\:{R}_{0}^{th}\)</EquationSource> </InlineEquation> exceeds one, for which local stability conditions are explicitly derived. These observations reveal the relationship between network topology, infection heterogeneity, and recovery strategies. The proposed framework, in addition to the advancement of theoretical understanding of malware propagation, also delineates a foundation for designing effective defence mechanisms to safeguard WSN infrastructure.</p>

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A Compartmental Framework for Analysing Malware Transmission in WSNs with Dual Infection Pathways

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Shilpi Agrawal,
  • Nupa Ram Chauhan,
  • Pramod Kumar Srivastava

摘要

Recently, Wireless Sensor Networks (WSNs) have proven their pivotal role across several domains, such as battlefield surveillance, patient monitoring, and climate data collection. However, implementing security solutions in WSNs is very challenging due to the inherent constraints of computing power, memory, and energy in sensor nodes. To develop a novel epidemic-inspired compartmental model, five unique states: susceptible (S), exposed (E), two infectious classes (I₁ and I₂), and recovered (R) (SEI1I2R), serve as the basis to capture the malware propagation dynamics in WSNs. In contrast to classical approaches, our approach introduces a dual infection model, where exposed nodes transition into either I₁ or I₂ with distinct probabilities, enabling the realisation of real-world-like conditions of two distinct malware behaviours. Furthermore, the effects of node density (ρ) and the communication radius (r) are also probed for malware transmission by integrating them with the infection rate explicitly. A key contribution of this research is the derivation of the basic reproduction number ( \(\:{R}_{0}^{th}\) ). It is considered a key threshold parameter that delineates the malware propagation in WSNs, apprehending the local dynamics of malware transmission. Furthermore, the expressions for threshold node density and communication radius are derived and validated through simulation results. Rigorous mathematical analysis establishes that the malware-free equilibrium is locally and globally stable whenever the basic reproduction number \(\:{R}_{0}^{th}\) is less than unity, whereas the endemic equilibrium emerges and remains stable when \(\:{R}_{0}^{th}\) exceeds one, for which local stability conditions are explicitly derived. These observations reveal the relationship between network topology, infection heterogeneity, and recovery strategies. The proposed framework, in addition to the advancement of theoretical understanding of malware propagation, also delineates a foundation for designing effective defence mechanisms to safeguard WSN infrastructure.