Impulsive Switching Epidemic Model with Benign Worm Defense and Quarantine Strategy

Jiying Lai,Xinzhu Meng,Shujing Gao,Yujiang Liu

doi:10.1155/2020/3578390

Jiying Lai, Xinzhu Meng + Show 2 more

Open Access

https://doi.org/10.1155/2020/3578390

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Abstract

The issue on how to effectively control Internet malicious worms has been drawn significant attention owing to enormous threats to the Internet. Due to the rapid spreading of malicious worms, it is necessary to explore the integrated measures to automatically mitigate the propagation on the Internet. In this paper, a novel worm propagation model is established, which combines both impulsive quarantine and benign worm implementation. Then, sufficient conditions for the global stability of worm-free periodic solution and the permanence of the benign worm are obtained. Finally, the effects of quarantine strategy are assessed and some feasible strategies that can constrain the propagation of malicious worm are provided by numerical simulation.

Highlights

With the wide use of computer network, network security problem, such as illegal access, malicious worm attacks, and virus spread, has become more remarkable and complicated
Since traditional prevention measures cannot e ectively constrain worm propagation, the way of using benign worms to ght against worms has been becoming a new emergency response technology. e idea of benign worm is to transform a malicious worm into an antiworm which spreads itself using the same mechanism as the original worm and immunizes a host [6]
We present a set of simulation results to verify dynamical behavior of the model and evaluate the effect of benign worm and quarantine strategy in defending against malicious worm. e numerical simulations are performed by MATLAB

Summary

Introduction

With the wide use of computer network, network security problem, such as illegal access, malicious worm attacks, and virus spread, has become more remarkable and complicated. According to the propagation mechanism of benign worms, many mathematical models have been proposed to analyze the transmission law and transmission trend of di erent worms in various real-life networks [1, 7,8,9,10]. In [16], an Internet worm propagation model with time delay in quarantine was proposed and theoretical analyzed. We mainly formulate a worm propagation model with impulsive quarantine and switching in time, study the dynamic behavior, and evaluate the control strategies. A brief conclusion is given and future research is put forward in the last section

Model Formulation

Global Asymptotical Stability of Worm-free Periodic Solution

Persistence of Benign Worm

Comparison of Four Worm Models

Conclusion and Discussion