A new analytic numeric method solution for fractional modified epidemiological model for computer viruses

Computer viruses are an extremely important aspect of computer security, and understanding their spread and extent is an important component of any defensive strategy. Epidemiological models have been proposed to deal with this issue, and we present one such here. We consider the modified epidemiological model for computer viruses (SAIR) proposed by J. R. C. Piqueira and V. O. Araujo. This model includes an antidotal population compartment (A) representing nodes of the network equipped with fully effective anti-virus programs. The multi-step generalized differential transform method (MSGDTM) is employed to compute an approximation to the solution of the model of fractional order. The fractional derivatives are described in the Caputo sense. Figurative comparisons between the MSGDTM and the classical fourth-order Runge-Kutta method (RK4) reveal that this method is very effective. Mathematica 9 is used to carry out the computations. Graphical results are presented and discussed quantitatively to illustrate the solution

The SEIQS stochastic epidemic model with external source of infection

This paper deals with a stochastic epidemic model for computer viruses with latent and quarantine periods, and two sources of infection: internal and external. All sojourn times are considered random variables which are assumed to be independent and exponentially distributed. For this model extinction and hazard times are analyzed, giving results for their Laplace transforms and moments. The transient behavior is considered by studying the number of times that computers are susceptible, exposed, infectious and quarantined during a period of time (0, t] and results for their joint and marginal distributions, moments and cross moments are presented. In order to give light this analysis, some numerical examples are showed

A Review of Mathematical Model Based in Clustered Computer Network

The threats produced by viruses in computer networks have been frequent and the subject of many studies. Computer viruses share common characteristics with biological viruses, and therefore, one of the ways to study the dynamics of virus propagation has been through biological analogies. Inspired by macroscopic models, the susceptible-infected-removable (SIR) model allowed variations of compartmental models and suggested defenses considering antidotal (SIRA) and quarantined compartments (SIQRA), giving rise to models that evaluate the effectiveness and strategies to control the spread of viruses in networks. Recently, with the rapid popularization and access to networks, new studies have been taken into consideration the clusters of association of networks, indicating new control strategies and particularities of the dynamics. Toward this goal, this chapter presents a review of the mathematical model based in clustered computer network with the brief overview of the mathematical model reviews and providing an integrated framework to clustered model. In this essay, there is a discussion about the several ways of applying compartmental models to study the propagation of computer viruses and malwares through networks, emphasizing the effect of connections between geographically distributed machine clusters

Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs

We investigate the various conditions that control the extinction and stability of a nonlinear mathematical spread model with stochastic perturbations. This model describes the spread of viruses into an infected computer network which is powered by a system of antivirus software. The system is analyzed by using the stability theory of stochastic differential equations and the computer simulations. First, we study the global stability of the virus-free equilibrium state and the virus-epidemic equilibrium state. Furthermore, we use the Itô formula and some other theoretical theorems of stochastic differential equation to discuss the extinction and the stationary distribution of our system. The analysis gives a sufficient condition for the infection to be extinct (i.e., the number of viruses tends exponentially to zero). The ergodicity of the solution and the stationary distribution can be obtained if the basic reproduction number Rp is bigger than 1, and the intensities of stochastic fluctuations are small enough. Numerical simulations are carried out to illustrate the theoretical results

Global Dynamics and Optimal Control of a Viral Infection Model with Generic Nonlinear Infection Rate

This paper is devoted to exploring the combined impact of a generic nonlinear infection rate and infected removable storage media on viral spread. For that purpose, a novel dynamical model with an external compartment is proposed, and the explanations of the main model assumptions (especially the generic nonlinear infection rate) are also examined. The existence and global stability of the unique equilibrium of the model are fully investigated, from which it can be seen that computer virus would persist. On this basis, a next-best approach to controlling the level of infected computers is suggested, and the theoretical analysis of optimal control of the model is also performed. Additionally, some numerical examples are given to illustrate the main results

Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses

We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks

Optimal Control of Multiple Transmission of Water-Borne Diseases

A controlled SIWR model was considered which was an extension of the simple SIR model by adjoining a compartment () that tracks the pathogen concentration in the water. New infections arise both through exposure to contaminated water as well as by the classical SIR person-person transmission pathway. The controls represent an immune boosting and pathogen suppressing drugs. The objective function is based on a combination of minimizing the number of infected individuals and the cost of the drugs dose. The optimal control is obtained by solving the optimality system which was composed of four nonlinear ODEs with initial conditions and four nonlinear adjoint ODEs with transversality conditions. The results were analysed and interpreted numerically using MATLAB

Awareness and perception of phishing variants from Policing, Computing and Criminology students in Canterbury Christ Church University

This study focuses on gauging awareness of different phishing communication students in the School of Law, Policing and Social Sciences and the School of Engineering, Technology and Design in Canterbury Christ Church University and their perception of different phishing variants. There is an exploration of the underlying factors in which students fall victim to different types of phishing attacks from questionnaires and a focus group. The students’ perception of different types of phishing variants was varied from the focus group and anonymised questionnaires. A total of 177 respondents participated in anonymised questionnaires in the study. Students were asked a mixture of scenario-based questions on different phishing attacks, their awareness levels of security tools that can be used against some phishing variants, and if they received any phishing emails in the past. Additionally, 6 computing students in a focus group discussed different types of phishing attacks and recommended potential security countermeasures against them. The vulnerabilities and issues of anti-phishing software, firewalls, and internet browsers that have security toolbars are explained in the study against different types of phishing attacks. The focus group was with computing students and their knowledge about certain phishing variants was limited. The discussion within the focus group was gauging the computing students' understanding and awareness of phishing variants. The questionnaire data collection sample was with first year criminology and final year policing students which may have influenced the results of the questionnaire in terms of their understanding, security countermeasures, and how they identify certain phishing variants. The anonymised questionnaire awareness levels on different types of phishing fluctuated in terms of lack of awareness on certain phishing variants. Some criminology and policing students either did not know about phishing variants or had limited knowledge about different types of phishing communication, security countermeasures, the identifying features of a phishing message, and the precautions they should take against phishing variants from fraudsters