Dynamics Analysis of Epidemic Computer Virus Models

In the present arena of digital world and Internet of Things, networks are becoming the target of well-crafted cyber-attacks especially, the incidents related to breach of internal system security and espionage of protected critical information. The computer viruses that can cause serious damage and compromise sophisticated systems have drawn special attention from the research community due to their masked and multifarious attack patterns. Removable storage media plays an important role in the transfer of data and virus to the computers connected to the critical networks. The air-gap between these networks are compromised by exploiting the internal weaknesses of the arrangement, transferring of data through removable storage media, hardware implants and zero-day vulnerabilities in the software / hardware that could be exploited in the real world before its disclosure. Thus, in a computer network virus poses a serious threat to the resource availability, confidentiality and integrity of critical assets. The purpose of this study is to design and upgrade the existing epidemic virus models under different conditions that describe the transmission of malicious computer code in active computer networks. An epidemic virus model that portray the spread of the malicious code in a critical infrastructure with pre-existing immunity and quarantine as an effective control strategy is designed. Due to the rapid spread of computer viruses and delay in the update of antivirus signature database, the role of quarantine as a controlling mechanism has gained importance. An epidemic virus model is designed that depicts the behavior of Stuxnet virus which is an advance persistent threat (APT) type cyber attack, uses unusual methods to attack resources with an intend to access the critical information while remains undetected and require special arrangement for control. Hardware based implants are common in these days gadgets and in computing machines for exploitation. Hardware implant based epidemic model is designed that portray the exploitation of hardware through embedded tiny chip. The control strategy of these compromised nodes are very difficult because they implant backdoors, install malicious utilities, gain admin rights, work as a legitimate program or infect with viruses. Nonlinear mathematical models are considered to analyze the dynamic behavior of such virus spreads which exploits the inability of antivirus utilities and zero-day bugs of the software / hardware systems. The existence of disease free and endemic equilibrium points are explored in terms of the basic reproduction number R0 for stability analysis. Numerical simulations are performed to investigate the dynamics of the models using well-established numerical techniques. Fractional order nonlinear models are designed for detailed analysis of the epidemic virus spread in the normal, air-gapped critical networks and hardware based implant vulnerabilities. Numerical experimentation’s for fractional order models are performed using Grunwald-Letnikov (GL) based numerical solver and results show that fractional order models provide enrich dynamics by means of supper fast transients as well as supper slow evolutions of the steady-state which are seldomly perceived in integer order counterparts. Models accuracy are evaluated by comparing the results with available observed real data, published results and exact solutions.


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