NONSTANDARD FINITE DIFFERENCE SCHEMES FOR SOLVING A MODIFIED EPIDEMIOLOGICAL MODEL FOR COMPUTER VIRUSES

In this paper we construct two families of nonstandard finite difference (NSFD) schemes preserving the essential properties of a computer virus propagation model, such as positivity, boundedness and stability. The first family of NSFD schemes is constructed based on the nonlocal discretization and has first order of accuracy, while the second one is based on the combination of a classical Runge-Kutta method and selection of a nonstandard denominator function and it is of fourth order of accuracy. The theoretical study of these families of NSFD schemes is performed with support of numerical simulations. The numerical simulations confirm the accuracy and the efficiency of the fourth order NSFD schemes. They hint that the disease-free equilibrium point is not only locally stable but also globally stable, and then this fact is proved theoretically. The experimental results also show that the global stability of the continuous model is preserved

The eigenpairs of a Sylvester-Kac type matrix associated with a simple model for one-dimensional deposition and evaporation

A straightforward model for deposition and evaporation on discrete cells of a finite array of any dimension leads to a matrix equation involving a Sylvester-Kac type matrix. The eigenvalues and eigenvectors of the general matrix are determined for an arbitrary number of cells. A variety of models to which this solution may be applied are discussed.Comment: 7 pages, no figure

ANALISIS DINAMIKA MODEL EPIDEMI SEIQR-SI PENYEBARAN WORM BEBASIS WI-FI PADA SMARTPHONE

Artikel ini membahas model matematika SEIQR-SI penyebaran worm berbasis Wi-Fi pada smartphone. Worm berbasis Wi-Fi termasuk perangkat lunak yang mampu mereplikasi dirinya untuk mencoba memecahkan kata sandi setiap router Wi-Fi baru yang ditemuinya tanpa bantuan manusia. Analisis model dilakukan dengan menentukan titik kesetimbangan beserta kestabilannya. Hasil analisis menunjukkan bahwa model SEIQR-SI memiliki dua titik kesetimbangan yaitu titik kesetimbangan bebas worm dan titik kesetimbangan endemik. Titik setimbang bebas worm stabil asimtotik lokal jika , sedangkan titik setimbang endemik stabil asimtotik lokal jika . Pada bagian akhir diberikan simulasi secara numerik yang menunjukkan peningkatan laju karantina oleh Wi-Fi base station pada worm dapat menekan jumlah node smartphone dan Wi-Fi yang terinfeksi worm

A novel dynamics model of fault propagation and equilibrium analysis in complex dynamical communication network

International audienceTo describe failure propagation dynamics in complex dynamical communication networks, we propose an efficient and compartmental standard-exception-failure propagation dynamics model based on the method of modeling disease propagation in social networks. Mathematical formulas are derived and differential equations are solved to analyze the equilibrium of the propagation dynamics. Stability is evaluated in terms of the balance factor G and it is shown that equilibrium where the number of nodes in different states does not change, is globally asymptotically stable if G≥1. The theoretical results derived are verified by numerical simulations. We also investigate the effect of some network parameters, e.g. node density and node movement speed, on the failure propagation dynamics in complex dynamical communication networks to gain insights for effective measures of control of the scale and duration of the failure propagation in complex dynamical communication networks

Spread of Malicious Objects in Computer Network: A Fuzzy Approach

We propose an e-epidemic fuzzy SEIQRS (Susceptible-Exposed-Infectious-Quarantine- Recovered-Susceptible) model for the transmission of malicious codes in a computer network. We have simulated the result for various parameters and analyzed the stability of the model. The efficiency of antivirus software and crashing of the nodes due to attack of malicious code is analyzed. Furthermore, initial simulation results illustrate the behavior of different classes for minimizing the infection in a computer network. It also reflects the positive impact of anti-virus software on malicious code propagation in a computer network. The basic reproduction number R0 f and its formulation is also discussed

Dynamics of a Computer Virus Propagation Model with Delays and Graded Infection Rate

A four-compartment computer virus propagation model with two delays and graded infection rate is investigated in this paper. The critical values where a Hopf bifurcation occurs are obtained by analyzing the distribution of eigenvalues of the corresponding characteristic equation. In succession, direction and stability of the Hopf bifurcation when the two delays are not equal are determined by using normal form theory and center manifold theorem. Finally, some numerical simulations are also carried out to justify the obtained theoretical results

Optimal control measures for a susceptible-carrier-infectious-recovered-susceptible malware propagation model

Purposing to lessen malware propagation, this paper proposes optimal control measures for a susceptible-carrier-infectious-recovered-susceptible (SCIRS) epidemiological model formed by a system of ordinary differential equations. By taking advantage of real-world data related to the number of reported cybercrimes in Japan from 2012 to 2017, an optimal control problem is formulated to minimize the number of infected devices in a cost-effective way. The existence and uniqueness of the results related to the optimality system are proved. Overall, numerical simulations show the usefulness of the proposed control strategies in reducing the spread of malware infections.- Fundação para a Ciência e Tecnologia, Grant/Award Number: UID/MAT/04106/2019 and UID/CEC/00319/201

Optimal Control of a Delay-Varying Computer Virus Propagation Model

By incorporating the objective of keeping a low number of infected nodes and a high number of recovered nodes at a lower cost into a known computer virus model (the delay-varying SIRC model) extended by introducing quarantine, a novel model is described by means of the optimal control strategy and theoretically analyzed. Through the comparison of simulation results, it is shown that the propagation of computer virus with varying latency period can be suppressed effectively by the optimal control strategy