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Mathematical analysis and design of the nonstandard computational method for an epidemic model of computer virus with delay Effect: Application of mathematical biology in computer science
Results in Physics ( IF 4.4 ) Pub Date : 2020-12-30 , DOI: 10.1016/j.rinp.2020.103750
Ali Raza , Umbreen Fatima , Muhammad Rafiq , Nauman Ahmed , Ilyas Khan , Kottakkaran Sooppy Nisar , Zafar Iqbal

Mathematical modeling with nonlinear delay differential equations (DDES) impart a significant role in the different disciplines such as epidemiology, computer modeling, immunology, physiology, neural networks, social sciences, bio-medical engineering, and many more. In this manuscript, a nonlinear delayed model is investigated to study the dynamics of a virus in a computer network. Many important results are established for the stability of equilibria of the model using the Routh Hurwitz criterion, Volterra Lyapunov function, and Lasalle invariance principle. Also, a nonstandard finite difference method is presented for the computational analysis of the model. The delay tactics like, be cautious while opening the email attachments, disable image previews in your email client, use an anti-malware solution, monitor all devices proactively, utilize administrator rights, pay attention to virus-related warnings and notifications, are precautionary measures which can help us in removing the virus from network. The impact of delay tactics on the threshold number is also analyzed. In the end, numerical results are presented to strengthen the theoretical analysis of the model.



中文翻译:

具有时滞的计算机病毒流行模型非标准计算方法的数学分析和设计:数学生物学在计算机科学中的应用

具有非线性延迟微分方程(DDES)的数学建模在诸如流行病学,计算机建模,免疫学,生理学,神经网络,社会科学,生物医学工程等等的不同学科中发挥着重要作用。在本文中,研究了非线性延迟模型,以研究计算机网络中病毒的动态。使用Routh Hurwitz准则,Volterra Lyapunov函数和Lasalle不变原理,为模型的平衡稳定性建立了许多重要结果。此外,提出了一种非标准的有限差分方法,用于模型的计算分析。延迟策略包括:在打开电子邮件附件时要谨慎,在电子邮件客户端中禁用图像预览,使用反恶意软件解决方案,主动监视所有设备,利用管理员权限,注意与病毒有关的警告和通知,这是预防措施,可以帮助我们从网络中删除病毒。还分析了延迟策略对阈值数量的影响。最后,给出数值结果以加强模型的理论分析。

更新日期:2021-01-10
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