Abstract
The popularity of the Web improves the growth of web threats. Formulating mathematical models for accurate prediction of malicious propagation over networks is of great importance. The aim of this paper is to understand the propagation mechanisms of web malware and the impact of human intervention on the spread of malicious hyperlinks. Considering the characteristics of web malware, a new differential epidemic model which extends the traditional SIR model by adding another delitescent compartment is proposed to address the spreading behavior of malicious links over networks. The spreading threshold of the model system is calculated, and the dynamics of the model is theoretically analyzed. Moreover, the optimal control theory is employed to study malware immunization strategies, aiming to keep the total economic loss of security investment and infection loss as low as possible. The existence and uniqueness of the results concerning the optimality system are confirmed. Finally, numerical simulations show that the spread of malware links can be controlled effectively with proper control strategy of specific parameter choice.
Highlights
The popularity of the Web improves the growth of web threats
Web-based viruses have become an increasingly attractive option for cyber-criminals to attack users without searching for new vulnerabilities in network services. They can spread in the form of hyperlinks which may exist in short messages or spam emails that lure victims to click on the malicious URLs and redirect to a false web page which is able to inject malware into their devices
Web threats are able to cause a broad range of risks, such as financial damages, damage of company reputation, and loss of consumer confidence in e-commerce and online banking[33]
Summary
The popularity of the Web improves the growth of web threats. Formulating mathematical models for accurate prediction of malicious propagation over networks is of great importance. Web-based viruses have become an increasingly attractive option for cyber-criminals to attack users without searching for new vulnerabilities in network services. They can spread in the form of hyperlinks (i.e., the addresses of corresponding harmful websites purporting to proliferate malware) which may exist in short messages or spam emails that lure victims to click on the malicious URLs and redirect to a false web page which is able to inject malware into their devices.
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