The open nature of Wireless Sensor Networks (WSNs) renders them an easy target to malicious code propagation, posing a significant and persistent threat to their security. Various mathematical models have been studied in recent literature for understanding the dynamics and control of the propagation of malicious codes in WSNs. However, due to the inherent randomness and uncertainty present in WSNs, stochastic modeling approach is essential for a comprehensive understanding of the propagation of malicious codes in WSNs. In this paper, we formulate a general stochastic compartmental model for analyzing the dynamics of malicious code distribution in WSNs and suggest its possible control. We incorporate the stochasticity in the classical deterministic model for the inherent unpredictability in code propagation, which results in a more appropriate representation of the dynamics. A basic theoretical analysis including the stability results of the model with randomness is carried out. Moreover, a higher-order spectral collocation technique is applied for the numerical solution of the proposed stochastic model. The accuracy and numerical stability of the model is presented. Finally, a comprehensive simulation is depicted to verify theoretical results and depict the impact of parameters on the model's dynamic behavior. This study incorporates stochasticity in a deterministic model of malicious codes spread in WSNs with the implementation of spectral numerical scheme which helps to capture these networks' inherent uncertainties and complex nature.

• Klíčová slova
• Spectral collocation technique, Stochastic compartmental modeling, Distribution density, Wireless sensor network, Malicious codes propagation, Stability Analysis,
• Publikační typ
• časopisecké články MeSH

The economic impact of Human Immunodeficiency Virus (HIV) goes beyond individual levels and it has a significant influence on communities and nations worldwide. Studying the transmission patterns in HIV dynamics is crucial for understanding the tracking behavior and informing policymakers about the possible control of this viral infection. Various approaches have been adopted to explore how the virus interacts with the immune system. Models involving differential equations with delays have become prevalent across various scientific and technical domains over the past few decades. In this study, we present a novel mathematical model comprising a system of delay differential equations to describe the dynamics of intramural HIV infection. The model characterizes three distinct cell sub-populations and the HIV virus. By incorporating time delay between the viral entry into target cells and the subsequent production of new virions, our model provides a comprehensive understanding of the infection process. Our study focuses on investigating the stability of two crucial equilibrium states the infection-free and endemic equilibriums. To analyze the infection-free equilibrium, we utilize the LaSalle invariance principle. Further, we prove that if reproduction is less than unity, the disease free equilibrium is locally and globally asymptotically stable. To ensure numerical accuracy and preservation of essential properties from the continuous mathematical model, we use a spectral scheme having a higher-order accuracy. This scheme effectively captures the underlying dynamics and enables efficient numerical simulations.

• Klíčová slova
• HIV infection, Legendre-Gauss-Lobatto points, Mathematical delay model, Spectral method, Stability analysis, Stochastic effect,
• MeSH
• biologické modely MeSH
• HIV infekce * MeSH
• HIV * MeSH
• lidé MeSH
• počítačová simulace MeSH
• základní reprodukční číslo MeSH
• Check Tag
• lidé MeSH
• Publikační typ
• časopisecké články MeSH